Full utility, cooldown reduction is great.
Improved ghost is a must as well.
250 Mana stone
2 healing potions
Boots of Swiftness
Frozen Heart/Zonya's Ring (if your games last this long I pity you)
Also possible to start with +7 mp5 and get the -10% cooldown/mp5/Ability power item (forget name). However sheen is essential and is needed it asap. It depends on how well you can creep, but if you return to base with enough money to buy sheen flat out get it instead of finishing the cool down reducer.
Sion is one of the best last hitters in the game (second maybe only to Annie). Activate enrage and never take it off. Solo or not isn't really that important, but the person you lane with needs to be okay with not getting many creep kills (Sion is going to take them all). Don't worry too much about the enemy champs early on, but don't stay at full mana, throw a stun on whoever has the least regen on the enemy side.
Stun them and hit them once. Your enrage packs a punch even at low levels and a lucky crit is a big deal. Staying in the lane until you have at least 1300~ gold is important (rough cost of sheen and boots, after initial mana stone). Your purpose isn't to kill them (yet), it's to keep you in aggressive positioning in the lane while u own them at creeping.
Get ultimate at level 6 if you need a heal, its not that great offensively for this build though.
Once you get sheen and boots of swiftness:
The fun begins. I prefer staying in a lane to push towers (which Sion is good at with his high physical damage via enrage). Begin by stunning and hitting champions only one time, as before. By level 8, your stun + hit in coordination with sheen should be pretty brutal, a 500 hp champ is killable in most situations. After a stun hit, only chase a champ if you believe that the next stun and hit will be a kill; getting three stuns off while chasing a hero is unlikely. Using ghost and blink can add another stun and hit into your assault, but is situational.
Build Magi's as soon as possible.
When you begin to level up shield it will be kind of useless for a few levels. I generally only use the shield at these low levels to create another proc on Sheen and/or if I have tons of mana. At level 3 it becomes powerful enough to merit consistent use. Using shield can take some getting used to. The idea is to put shield up before you enter the fight, so that after you stun someone and run in your shield explosion will happen before the stun wears off. As your ability power gets higher, shield can also be used defensively, but in general you don't want shield to expire from damage, you want it to explode.
Late game/team fights:
This Sion is not a tank. You can not engage first without heavy support. Stay in the back with the other ranged on your team waiting for moments to throw a stun. If the target is in good position run in to do your sheen proc'ed hit, then ult to proc sheen/lichbane, then, if off cooldown, use shield to proc another sheen/lichbane. After these three sheen/lichbane hits, your damage is done until the next stun is off cool down which, ideally, is thrown at max range. Get out of the battle after your initial burst, unless your team has a big advantage, ofc.
Alternatively, if Sion has heavy support behind him (Soraka, Zilean, Morgana, or any significant aoe stun), using shield and blinking in as it is about to explode can be a good aoe burst to start the fight, but afterwards its usually a good idea to throw your stun, hit once, and then get out. Your ultimate would probably not get you through more than one person focusing on you.
Make sure your team knows you're building a caster Sion, and explain that you can not initiate team battles easily. Be verbal about when you have extinguished your damage sequence of stun hit ult hit shield hit so your team knows you can not stay in to take hits.
The order of leveling stun and enrage can be played with, more creeping means level enrage.