I've played a lot of Sion as both AP and DPS (which are both very viable) but I noticed a lack of good AP build on here so I thought I'd put one together. Its worth noting that I'm a very aggressive player and this build matches that mindset. I'll give some alternatives but I haven't tested them as much.
Summoner Skills -
Ghost - My favorite summoner skill on Sion is Ghost. Since he already has his built in block, shield, and max hp farming I find he doesn't insta-explode as much other casters. With Ghost up you can frequently stun their scariest player, put up shield and dash out of a gank. On the offense your 2sec stun can dominate players trying to flee if you can get within range, and that Ghost will generally let you catch them. Then either you can finish them off, or your team will catch up and its all over. Mmmmm
My second skill is a toss up between Cleanse and Exhaust.
Exhaust - It is awesome for keeping your shield up verse a massive DPS character in a 1 on 1 fight, plus that slow with your stun means no one is getting away.
Cleanse - On the flip side, Cleanse has saved my life more times than I can imagine. It can save you from a myriad of focused kills which I won't bother to describe. I'm sure you can figure this part out.
Other skills you might consider would be Flash, Ignite and Teleport.
Flash - I prefer the extended fleeing/chasing power and shorter CD on Ghost, but the ability to Flash through walls can be invaluable.
Ignite - It helps your insta-gibs and also can be invaluable against enemy healing (regen/heals/lifesteal). If your team is short on Ignites then grab this and do even more raw damage!
Teleport - It doesn't have the direct combat utility of the others, but AP Sion is a monster farmer with his shield and his stun can make or break ganks. So if you feel confidant with your ability to succeed in fights then take Teleport so you can be wherever the creeps are the densest or the fights are happening.
Since I'm crazy and don't actually get any mana items (until the very end) the 5 mp5 and extended neutral buff durations of the Utility tree are key parts of this build. Still, a 21 point defensive build could also work very nicely but you might have to itemize for mana earlier and/or be more conservative with your casting. The 9 points in Offense are non-negotiable though. That extra AP/CDR/MrP are all too good to pass up.
Marks: I chose the magic penetration because this build utilizes a lot of flat MrP. The interesting thing about magic resistance having diminishing returns is that it makes magic penetration have increasing returns as you stack more of it (assuming you don't try to drop them below zero). Once you have boots and the guise that'll give you 51 MrP which is about a 25% increase in damage!
Seals: I've switched this to use mana per 5 instead, since early mana regen is a huge issue for Sion. If you'd rather take hp or dodge or armor instead, that might work though it'll reduce your ability to spam your shield/nuke.
Glyphs: MOAAARR DAMAGE!! We want to hit like a truck, and these bad boys help you do just that! The AP per level give over 3x the AP of the flat ones, and they'll have already caught up by lvl 6. That's about all there is to say.
Quints: More flat MrP here since this build focuses around having the awesome percent damage boost that comes from penetration. Your items will get you plenty of AP anyway.
(passive) Feel No Pain: This skill alone makes Sion more of a tank then he has any right to be, and its totally free! It can allow you to shrug off large amounts of minions (great for those early ganks) and generally soak more damage than your hp bar implies you should.
(Q) Cryptic Gaze: At this start this skill is used to primarily for its 2 sec stun utility. Its an awesome way to start fights and often to finish a chase too. This skill will get you (or your lane mate) first blood. Later on as you finally max it's rank it'll become a major part of your damage output and continuous control. With full CDR its got a 5 sec cooldown meaning you can keep someone stunned for 40% of a fight! Combined with an exhaust you can shut down a carry for 7 straight seconds!! (stun, exhaust, stun)
(W) Death's Caress: This is easily one of the best AOE spells in the game. It not only gives you a massive area of effect with a full 1x AP multiplier but it also gives you a damage shield for the same amount! By leveling this first you ensure that you'll be damned hard to kill and able to farm like crazy. You'll find very quickly that you'll be able to wipe entire creep waves out in one blast making you an amazing pusher and helping you rush your items. Don't hesitate to jump to unattended lanes and just obliterate all the creeps.
(E) Enrage: This skill is a great one, but not as useful for our AP build. Still, it allows our caster fellow to hit fairly hard when he's not casting and should always be left on. Also its worth noting that you get the bonuses to your max HP even if you kill something with your spells (like say the entire creep waves I mentioned before with Death's Caress O_o)
(R) Cannibalism: Like enrage this skill is geared more for a AD build, but its certainly not without use. Its awesome for grabbing lizard/golem, healing yourself and teammates between fights, or in a close fight (ie. where you're not just running people down) that extra hp swing gained between casts can be invaluable. Since its not a part of your major damage rotation don't hesitate to use it just to heal up the team or take out towers.
Playing Sion and Items -
So start off with a lovely Doran's ring and health potion. Right from the get go you'll have 26AP, 10 extra Mp5 and almost 700 hit points! Combined with your passive you'll be very hard to kill, even when you dive into their minions.
Now I recommend you try to get the lane with the golem in it so you can nab it at 6, but its not necessary. You'll just have to gank the other lane after you grab it otherwise. Also try to lane with another character with early gank potential for that first blood. That means people with a nuke and/or CC. Then head up into the bushes and prepare to gank. Hopefully you get there before the other team in which case you should wait for them to advance at least up next to the wall halfway between the river and the tower range. Open up with your stun and right as it wears off hit them with the exhaust. If your buddy can deliver a little extra damage, FIRST BLOOD! If you instead engage them in the bushes essentially you should do the same thing, just be ready to switch targets if your other opponent over commits. Don't forget that at this point your passive essentially allows you to shed 40% of attacks against you, so be aggressive!
Once you start leveling your shield use it as your main harassment (NOT gaze). Keep going into the bushes, activate your shield and then wait the 4 secs for detonation potential. If you think you can get a kill feel free to gaze an opponent, but otherwise just run out into their mobs/players and detonate it. You should be able to nick most the mobs and clip the enemy players too! if they look like they're gonna hit you then wait for your shield to absorb some of that before detonating. Make them realize the futility of attacking Sion ;) You can even harass them in tower range with this since it'll absorb the tower hit, just make sure you time it well (and they don't stun/taunt your *** in there).
You should hopefully be able to stay in the lane all the way up to level 6 by making sure you're only in range of them when your shield is up, or they're fleeing as you run their frail ***es down. Either they'll have to stay at the back of their lane, or you'll eventually gank them with your 2 sec stun and massive nuke.
Now that you've hit 6 head back to base after draining you last mana to blast some creeps/players. I generally like going straight for the soulstealer if I find myself getting a lot of kills (and some of the other lanes look gankable), but you can switch the order of those first 3 items around if you need the HP and/or move sooner. Now on your way back to the fight make a pit stop at the golem and beat his face in with your shield and then ultimate. It takes a little experience to figure out how many hits you can absorb on your shield before you detonate it, but try to avoid losing that extra damage from the mobs knocking it to zero. If all goes well you should walk out with full hit points and essentially unlimited mana!
Now communicate with your team and start hunting players everywhere. If you can leap out of the bushes with a Q/W combo you'll generally get a kill (though make sure you know who has cleanse!). After you get a kill or maim in a lane use your massive AOE damage to push right up to the turrets and demolish them. The less first tier towers the have the easier your ganks will become.
Your next items should be Haunting Guise and Nashor's Tooth. Haunting Guise is an amazing item with its increase to your HP, another 20 MrP (should bring you up to 51!) and 25AP to top it off. Nashor's Tooth has more mana regen to let you stay out in the field longer, a respectable amount of AP, a huge 25% cooldown reduction (with puts you at 34% with masteries, almost at your cap) and the attack speed which is just icing on the cake with your Enrage.
I haven't tried Deathfire Staff instead of Nashor's, but I think that could be amazing for insta-gibbing opposing champions. If you do go for it then I'd recommend chugging the blue elixir with it so you can still hit 34% CDR. I'll try this out and let you all know.
From here out I don't have much more to say strategy wise that you shouldn't already know. Farming wise just keep hitting those empty lanes where the creeps have built up and try to keep the golem buff up as much as possible. Your main goals in team fights are to get your stun off on a squishy but lethal target and follow up with an AOE that hits a majority of their team. Also if it looks like you won't have to do hit and runs then activate your ult and start swinging between casts. You hit relatively hard for a caster.
Note that your shield does add a lot to your survivability but make sure you don't initiate full team fights. It probably won't save you from an entire angry team (they are angry right? You've been eating their faces), and even if you do survive, your damage potential receives a brutal kick to the nuts when they pop your bubble. So stay back for a second after a fight starts before diving in to AOE. The trick is balancing how long you leave shield up to protect yourself and detonating it early enough to let you get more of them off in a fight.
Up next you'll want to get Lich Bane so you can get more out of your large AP pool. You can almost double your damage output if you intelligently space out your spells to take advantage of the proc. Of course if you're having survivability issues or your opponents are rocking too much MR then grab whatever seems necessary.
If the game isn't over by now then you should work towards Zhonya's Ring for its awesome damage increase and ability to slap death in the face. Don't hesitate to pop that sucker if you're getting focused, you'll not only disrupt their team's coordination but also give your spells another 2 seconds of cooldown to help you get back out!
Proof of Success-
Just to make sure I wasn't talking ******** here I played this exact build quite a few times over the past few days. He's scary if you're team isn't doing well, and absolutely horrifying if they are :)
Win - 9/2/7
Loss - 6/3/5 << even when your team is feeding like crazy, you can still kill their cocky carries :P
Win - 10/1/5
Win - 4/4/7 << a bit suicidal here, oh well :D
Win - 8/4/13
Win - 12/3/8
Sadly I don't think Sion will often get monsterous 15+ kill games because he's not the best last hitter in a team fight and when he does get rolling most people surrender. Still, you'll find that he really changes the game even if he can't get the killing blows on everything. You'll often be able to solo everyone on their team, and your presence will destroy them in full team fights. Hopefully you enjoy crushing the puny little men arrayed against you!
What is best in death? To crush your enemies, see them driven before you, and hear the lamentation of noobs!