This is my AP Sion build. I am by no means a highly ranked player, but I do fairly well at my elo with this build.

Sion is a great, I almost always pick him in ranked if the enemy team has a Katarina, malz, ww, or any other champion that has a channeled ultimate. You can ruin a Katarinas day in almost every team fight by just waiting for her to ult and stunning her.

For runes I like magic penetration marks, mana regen per level seals and flat CDR glyphs. For quints I go HP, but magic pen or even armor pen works here as well.

For masteries I like a fairly basic caster build, taking a point in imp flash and two in extended buff duration.

Sheen - Boots of choice - Rabadan's Deathcap - Nashors Tooth

*NOTE* I do not have Rabadon's Deathcap in my item purchase order, please read here to find out where it goes.

For items I start with Mana Crystal Mana Crystal + x2 HP pots

I then go back for boots and Sheen + x2 and sight ward Usually around 1300-1500 gold(minimum 1300).

If you are doing well farming your lane, tower hug and try to farm for a Needlessly Large rod. If you have to go back and you dont have enough for a then just grab a

Once you have your Rod and Wand, you will be able to farm creep waves with just your shield. Continue to farm and play passively til you get your Rabadon's Deathcap

Your build order after that will be Boots of your choice(if they have taunt or fear its definitely worth it to get Merc Treads, if they stack magic resist then grab Sorc Boots).

Late game you will want some CDR, I personally like to build a Nashor's Tooth which will put your CDR around 35% with masteries.

The game will be close to over and you should upgrade your Sheen to a Lich Bane. I love the movement speed and your proc attacks will hit for almost 600.

If the game still isnt over grab a defensive item or whatever the sitiuation calls for, your AP will be ~475 with your shield hitting like a truck.

Early Game

The best way to farm with AP sion is in a solo lane. I usually only play sion if I can get solo top. Early game you want to use your shield to tank any ranged attacks while getting last hits. Last hits are EVERYTHING to this build. Having a large HP pool will help you late game. If you are laning against a squishy champion, taking an early stun for a stun->bubble combo or 2 will make your farming much easier. Typically your skill priority will be R-W-E-Q(*note, alot of people dont like to take Sion's ult until they have to, but it is extremely helpful when pushing a turret or trying to get blue quickly). I put 1 point in stun before level 6 and do not prioritize it since the stun is the same duration at all levels. At level 6 use your ultimate to farm and keep your HP up, you should have minimal mana issues as long as you dont spam stun.
Once your shield is high enough level you will basically be able to 1 shot whole creep waves, making farming a breeze and letting you farm your first core item before buying your boots.

Mid Game

If your lane is pushed, try ganking mid or throwing a ward at the enemy blue, sion has great burst potential in early game and the extra CDR with nashors tooth puts you right below the cap so your shield and stun cooldowns are quite low. Use your ult on towers and any time there is a team fight, regardless of weather you are low or not. The extra healing can really help your team.

Late game

If you farmed well then you should have a very nice HP pool and quite a bit of ability power. You should very rarely initiate and always have your shield ready to pop before you run in. When a team fight starts, flash into their carries, stun them and blow your shield and ultimate. Your shield will do significant damage to most of the team and you should help your team mop up

Pros
Lots of burst damage
Fun to play
A tanky caster
Easy to farm with

Cons
Hard to carry with him
If the enemy team blows your shield before you can open it blows your whole combo
Not very good against tanks
Hard to farm a 2v2 lane, killing enemy champ is helpful gold wise, but not so great for your HP pool.

All in all, Sion is one of the funnest champs to play IMO. He is a burst capable caster with a giant HP pool and an auto attack that hits for 250+ in late game.