I like my guides to the point and I dislike people telling me how to play so this guide will be very concise. I have put a good amount of testing into the build and assuming you are playing even slightly decent, you will have infinity edge by 30 minutes easily. Build is as follows.
All critical damage (55%)
3/3 Deadliness (More crit chance!)
1/1 Cripple (Exhaust is your friend@)
3/4 Sorcery (Cooldown. sure, why not?)
4/4 Alacrity (Hit faster!)
3/3 Sunder (More armor penetration!)
3/3 Brutality (More damage!)
3/3 Lethality (More crit Damage!)
1/1 Havoc (More Damage!)
3/3 Perseverance (This will help your regen a little)
1/1 Spatial Accuracy (speeds up your teleport a little)
4/4 Awareness (you would be amazed what 5% experience can do)
1/2 Utility Master (you will pick up a lizard here and there, this helps)
This is where freedom of choice comes into play but for how we set up masteries, I recommend
Though, these are dependant on my team. Make sure to ditch the exhaust mastery for archmages savy if you take exhaust off. I also have great success with Flash so really, either is viable. Teleport is pretty much a must with Tryndamere since you want to farm alot with him. Also, spinning into the jungle and teleporting to a new lane is fantastic to escape a gank.
3. Mocking Shout
4. Mocking Shout
5. Mocking Shout
6. Endless Rage
From here, prioritize Mocking Shout over Bloodlust over Spin.
This is where this guide differs a tad bit from standard guides.
-Opening item - Brawlers Gloves and health pots
-Go back as soon as you can turn them into an Avarice Blade
-Wait for teleport to Cooldown and go back for second Avarice Blade and as much of the BerserkersGrieves as you can afford. You don't want to miss any farming. Finish the boots at some point before the next step.
-Now comes the waiting. You will be waiting on a BF Sword, then Cloak of agility, THEN Pickaxe. Turn these into a sweet Infinity Edge. I regularly get the edge at minute 29 or 30 which is pretty fast Considering your items.
(current crit rate is 48.55%(+.25% per level) with 315% damage on crits.)
After this, you probably want to start into a Phantom Dancer starting with Zeal, then Cloak of Agility. Feel free to fill all empty slots in your inventory with Brawlers Gauntles as you buy things.
I would not reccomend selling your Avarice blades as they give alot of crit chance. Only sell them late game when they are wasting slots that could be filled by Executioners Calling or another Zeal / Agility Cloak.
With this build, you should get extremely high crit rates very easily with Bloodlust and items very early on and be truly terrifying. Anything that runs from you past your BF sword is basically a goner as you can Mocking Shout + Exhaust targets and auto attack for a very long time (note, doing both of these at once with the new slow cap is very foolish. Use exhaust between shouts)
When you lane with someone (probably better than you don't solo) tell your lane partner not to compete directly with you for a last hits as you need them to heal. This doesn't mean they shouldn't last hit at all but they should definitely not take last hits that tryndamere is already at and could pick up easily. It is imperative that you get at least 2 last hits a wave to keep bloodlust healing you. If you are not good with bloodlust, you will not last very long in your lane.
Once you have mocking shout, use it at every instance your opponent turns his back on you. This doesn't mean go for an attack but the damage decrease and human psychology will slow their farming WAY down. Almost every player you shout against will do nothing but run straight away from you until their slow comes off. At this point, they will turn directly around. You should be aware of this and if its safe, get right in their face as they turn around to return to the line. This will scare them again and should overall lower their farming rate way down. If the player is clearly not afraid of you, do still should at them alot, just don't risk yourself by threatening.
EARLY GANKING AND CONTROL
It is important to poke your enemy every once in a while to get a feel for your damage on them. Should they push you a distance, you may regain ground by spinning at them, this will almost gaurentee they turn around, shouting and then auto attacking them in the back until they unslow. If you are really laying on the damage, go for the exhaust after the shout and try to net a kill. Hopefully a crit comes along somewhere in there for a fat 180 damage.
Farming away is great here. With some ranks in bloodlust (which can optionally be taken at level 7 and 8) you want to try to look for opportunities to free farm a wave or two. Small neutral camps are easy to pick up with Tryndamere and he rarely net loses life from them with bloodlust.
Not much to say here. Be present at team ganks. Shout at your targets retreat in team ganks and crit everyone around you for tons of damage. Don't be afraid to get crazy in a fight when your ultimate is ready.
Okay, this part is really hard to explain. It just takes practice. Once you are level 6, you can bait insanely well. Getting people to attack you at your tower, surviving with your ultimate and using exhaust + mocking shout to make them eat turret fire will work ALOT more often than you think it will. The most important part of baiting is being intelligent and asking yourself, "Would I go for them right now?" if the answer is yes, I reccomend you keep a finger resting on your R key.
I have had a great deal of success playing this build of Tryndamere.
If you have any questions about playing him, item order, or just general strategy, feel free to ask here. I will try to give this guide good support.