Before you read this, lets get one thing straight. Galio is not a tank, he is not a caster DPS, he is not a support. He is all three. Galio is a multi-purpose champion that is good at everything and great at nothing. YES, sometimes you will get fed and turn into a damage machine and YES, sometimes the enemy team won't be able to kill you no matter how hard they focus you. Still, don't try to build Galio for one thing; build him for everything.
Also, please note that this is a full, comprehensive guide. I am assuming you know nothing about about Galio, his abilities, tactics, etc. Be prepared for a good length read, but feel free to skim. I tried to write the guide so that you can just read one section and understand what I'm talking about.
tl;dr: GUIDE LONG
Anyway, you will like Galio if you:
Like being able to help your team and dish out damage while staying completely out of the fight.
Enjoy shielding your carry from certain doom while simultaneously healing yourself.
Like being able to escape from nearly any situation, no matter how dire.
Like being able to incapacitate the entire enemy team for two and a half seconds, before dishing out a truly unfair amount of damage to them.
Like taking out an entire wave of minions with a single spell.
Enjoy finishing most games with somewhere between zero and two deaths.
Like having as many assists as your team has kills. (If you have a good team, you will probably have about one fifth as many kills as you do assists. If this bothers you, then Galio isn't for you)
First off, since I know a lot of people like to just get an idea of what items they should use, here the barebones item build I recommend:
Chalice of Harmony
Boots of Speed -> Mercury Treads
Banshee's Veil or Aegis of the Legion
There you go, you can leave now. If you are interested in more than that, however, or want to read the reasoning behind it, then read on, dear friend, read on.
Passive- Runic Skin: Galio gains ability power equal to 50% of his total magic resist.
This is a solid passive, and will guide how your build Galio (item wise). It is useful because it isn't just bonus magic resist; his base magic resist also contributes, meaning Galio has the highest starting ap of any champion in the game.
Resolute Smite: Galio fires an AoE blast at a targeted area, dealing 60/115/170/225/280 (+0.6 ap) damage and slowing enemies in the explosion radius.
Cost: 60/65/70/75/80 Mana
This is a good skill for catching fleeing enemies or slowing pursuing enemies, but can be a bit tricky to aim. It is also useful for farming.
Bulwark: Galio shields himself or an allied champion for 4 seconds, increasing their armor and magic resist by 30/45/60/75/90. Each time the shielded unit takes damage, Galio is healed for 20/32/44/56/68 (+0.3 ap) health, with the healing amount decreasing by 20% for each consecutive hit.
Cost: 60 Mana
This is an absolutely phenomenal skill. At level five, this can make it so enemy skills, especially dots, actually heal Galio for more damage than he takes.
The main purpose of this skill, however, is to protect whoever the enemy team focuses, probably your carry. 90 armor and magic resist transforms a glass cannon into the death star (minus the stupid exhaust port). Keep in mind that if you shield someone and they get a kill, you get an assist, even if you were completely out of the fight. In a teamfight, here are you priorities for shielding:
1. A teammate who has a very good chance of dying in the fight.
2. The teammate who will get the most kills.
The advantage of shielding yourself, even if you don't take that much damage, is that the increase in magic resist also becomes an increase in ap, giving you an edge damage-wise.
Righteous Gust: Galio sends a blast of wind that damages all enemies it passes through and leaves a wind tunnel that increases the movement speed of allies who travel in the same direction as it.
Damage: 70/115/160/205/250 (+0.8 ap)
Range: 1000 (the LoL website says 10,000, but I'm pretty sure that's a typo)
This skill is Galio's bread and butter. This will be your main ability for farming and damaging enemies. Although Resolute Smite has a lower mana cost and higher base damage, Righteous Gust is better for two reasons: It has a significantly higher ap bonus, and it is much easier to hit enemies with.
Early game, you will use this move to both last hit minions in the back and to harry the hell out of the enemy team. Once you get chalice of harmony, you can pretty much spam this move to your heart's content. The only downside to Righteous Gust is the cooldown; it is something like 12 seconds.
Somewhere around level 11, depending on how the game is going, you should be able to kill caster minions in one shot with this move.
Ultimate- Idol of Durand: Galio turns into a statue, blocking 30% of incoming damage while channeling an area taunt that lasts for 2.5 seconds. Once he stops channeling, Galio deals 220/330/440 (+0.85 ap) damage to all enemies in the taunt radius. This damage increases by 10% for each attack landed on Galio while he was channeling.
Cost: 100/145/190 Mana
This is an absolutely fantastic ultimate. Galio has the ability to stop a huge group of enemies from really being able to do much of anything. This ability is comparable to Amumu's ult, the difference being that Galio's has a smaller radius but larger damage.
If you can, always make sure you have bulwark active on yourself before you use this skill. It will make it so you take almost no damage, while also hitting them for even more damage at the end, since bulwark gives you an ap boost. Also, keep an eye on which enemies have mercury treads; those boots are the bane of your existence, since they can allow the enemy team to step out of the taunt before it finishes.
There are three situations where you want to use this skills:
Save yourself or a teammate
Incapacitate a huge chunk of enemies
Hold an enemy on a turret
Save yourself or a teammate: If a teammate is being pursued, or you are being focused and are about to die in a teamfight, consider popping your ultimate. In the first case it will buy your teammate valuable time to escape, and in the second it will decrease the amount of damage you take while keeping enemies from being able to cast.
Incapacitate the enemy team: This is the most straightforward use of Galio's ultimate. If there is a huge chunk of enemies standing together, flash in the middle and use Idol of Durand. It will keep them in one spot for easy pickings from your teammates. This move in great in conjunction with other over-time AoE's, like Gangplank's ult or Morgana's oil spill.
Hold an enemy on a turret: This is my least recommended use of Idol, but can be helpful if the enemy team is being a bunch of cocky jerks, especially a character like vladimir or katarina. They run in to turret dive, you taunt them and keep them there, making them take damage not just from your ult, but the turret as well. Fun times.
Masteries, Runes, and Summoner Spells
Masteries: I typically go for 9/0/21, but 9/21/0 can also work, depending on your preferences and playstyle. If you are in a purely supporting role and staying out of most fights, go with 9/0/21, but if you are needed to act as a tank by your team, go with 9/21/0. I will list my recommended masteries for both setups.
Offense(for both builds):
3 Archmage's Savvy
1 Archaic Knowledge
3 Strength of Spirit
1 Defensive Mastery
3 Harden Skin
4 Veteran's Scars
1 Spatial Accuracy or Good Hands (depending on if you are using teleport)
4 Expanded Mind
1 Blink of an Eye
1 Presence of the Master
Runes: The rune build for Galio is pretty straightforward. For marks (red), go with magic penetration; the damage bonus is pretty nifty, especially when combined with the Archaic Knowledge mastery. For seals (yellow) you are going to want flat armor, since you need armor early game when bulwark is a low level. For glyphs, either go with flat magic resist for increased ap or cooldown reduction. I personally recommend cooldown reduction, but they are so freaking expensive. For quintessence (black), go with flat health. Starting the game with +100 base health is just too good to pass up.
Marks: Magic Penetration
Glyphs: Magic Resist or Cooldown Reduction
Quintessence: Flat Health
Summoner Spells: For Galio, flash is a must. Period. There will be no negotiation on this point. Being able to flash into a mob of enemies and then use his ult is one of the things that makes Galio as good as he is. Your second summoner spell is up to you. I typically recommend teleport, unless your team already has at least two people with it, in which case I like to go with ignite. Teleport is nice because you can go back for items without missing out on too much exp and money, as well as for protecting a turret (Galio is amazing at wiping out huge groups of minions). Ignite is fun for getting even more assists and maybe even a few kills.
Other options are:
Fortify: A good skill for someone on your team to have, though teleport is honestly more useful for protecting turrets.
Cleanse: Always a decent skill, though as Galio, being tanky like you are, you really shouldn't need it.
Exhaust: A useful ability, though not one I'm a huge fan of.
Heal: Useful for being a support, but with bulwark you probably won't need the healing yourself.
Summoner Spells you should never use/need with Galio:
Ghost: Between Resolute Smite and Righteous Gust, you have more than enough pursuing/fleeing power.
Clarity: If you are having trouble with mana, use the support masteries build. If you are still having trouble with mana, then you are doing it wrong.
Smite: No. Get out. If you want smite on Galio, then you misunderstand this champion on such a fundamental level that you should never even be allowed in the same game as someone playing Galio. You might corrupt his skill with your failure.
Revive: See Smite.
Let me start by saying that this build aims at giving Galio as much ap and magic resist as possible. Keep that in mind.
You should start the game with a meki pendent. You can grab potions if you want to, but you honestly shouldn't need them. Upgrade that into chalice of harmony; this is just an amazing item, especially for Galio since he gets a small ap boost from it as well.
Next get boots of speed, but don't upgrade them just yet.
If you are feeling confident, get Mejai's next. Galio is so good at surviving and getting assists, you should be able to build it up no problem, even in a game where you team is less than phenomenal.
After boots/Mejai's, get Abyssal Scepter. I cannot stress enough how AMAZING this item is on Galio. It increases his ap, increases his magic resist, which further increases his ap, and reduces the magic resist of all enemies in the area. Man, that sure would be useful if you had, oh I don't know, a massive area damage move that forces enemies to stand around you.
Next upgrade your boots into mercury treads. No, not sorcerer's boots. I don't care how much your big brother likes them, get mercury treads.
A brief word about ninja tabi: At the end of the day, I can't make you pick mercury treads, but please, even if you don't get them, DO NOT get ninja tabi. Your ultimate requires that enemies hit you in order to increase damage. Ninja tabi sabotages this. That is all.
From this point on the game is pretty situational:
Typically I go with banshee's veil, since it adds magic resist (and therefore ap), as well as an absolutely delightful quantity of health and a phenomenal shield.
If you are stacking Mejai's like a fiend, however, you may want to with Zhonyas.
Deathfire Grasp is useful if you want some extra damage output and cooldown reduction.
If you and your team is having survivability issues, aegis of the legion is a great choice, especially if the enemy team is AD heavy, since it provides an armor bonus that this build otherwise lacks.
If the enemy team is basically all attack damage, and you are feeling reckless, you may want to give thornmail a try. The armor bonus is huge, and it makes Idol of Durand a hell of a lot more deadly. I don't really reccomend this, though, unless they haveat least two good AD champions, and probably not unless they have three.
Anyways, in summary, here is a rough idea of what your finished build should look like:
Chalice of Harmony
Boots of Speed -> Mercury Treads
Banshee's Veil or Aegis of the Legion
Idol of Durand
Idol of Durand
Idol of Durand
This build works by building up Galio's two best skills early, while leaving resolute smite at a low level. See, resolute smite, while being a good skill, just won't do as much damage to the enemy team since it is so easy to dodge. It is very useful, however, at level 1 for the slow. If you were to spam resolute smite and righteous gust every time you had the cooldown, you would run out of mana too quickly. Only use resolute smite when you need to slow to catch a fleeing enemy or to give a teammate a chance to escape.
Early Game: Start off by harrying the hell out of the other team with righteous gust. You probably won't get a kill in this way (unless you have a good lane partner or your opponents are just dumb). Focus on last hitting minions and keeping the other team away from the minions (and therefore gold and exp). If you got teleport, blue pill back to base and grab chalice of harmony as soon as you have 500 gold, then teleport back in. If you didn't choose teleport, wait until you have 850 gold, then head back for both chalice and boots of speed. Just keep harrying and last hitting until level 6.
Mid Game, Late Game, and how to behave in team fights: Once you have Idol of Durand, the fun begins. You should still spend most of time in your lane, farming, but your main goal is to always be in every fight. This will let you stack Mejai's quickly, as well as keep the other team down. Remember, Galio is a tank, a caster, and a support character all rolled into one; you need to be able to switch rolls instantly to adapt to the situation. If your teammates are dying, use your shield and spells to protect them. If your team isn't dealing enough damage, blast the enemies with spells. If your team is too soft to take out the guy hiding behind the turret, throw up bulwark on yourself and dive in there like a madman. Galio's playstyle really doesn't change much from mid to late game; the only difference is you can start spamming resolute smite as well as righteous gust, once you get its level up and have a really deep mana pool.
Galio is so good because he can do EVERYTHING. He can tank, he can farm, he can gank, he can shield, he can damage, etc. The only thing he is bad at is actually bringing down towers, but he takes out minions so efficiently that that really shouldn't be a problem.
A few tips and tricks:
If you are low on health and have bulwark maxed, go find the wraiths/wolves in the jungle. Throw up bulwark then attack them, once. Let them hit you till bulwark wears off; then wipe them out with righteous gust. You should heal for about 1/3 your health this way.
Don't forget about righteous gust's increasing movement speed component. It isn't much, but it can mean the difference between catching a fleeing enemy and letting him get away.
Remember to always be adaptable, and assist your teammates in any way you can. An average score for a well played Galio should be something like 5/1/25. You aren't going to get a ton of kills unless the enemy team feeds you. Just accept that and know that you are the engineer of your team's victories. Don't worry, you will be appreciated when you shield your carry from karthus's ult, allowing him to limp away with ten health and his stacks intact.