This guide should provide you with everything you need to know to play an AP Sion, which happens to be my favorite champ to play in LoL. It has a little strategy, an item build, runes, summoner spells, a strategy and skill build, and an idea of what your mastery should look like.
Laning
In my opinion, it shouldn't be hard to solo but if you can't get it or are laning with someone else by choice, try to lane on the side with the golem. This way, you can kill the golem without going out of your way. You should be able to kill the golem very easily with your ult and don't be afraid to use all your mana because the golem buff will give you your mana back. This build is very mana dependent and so any chance that you get, you should get the buff. The cooldown reduction is also very useful to get the stun more often.
The items that I get are as follows;
1. Start with a sapphire crystal and 2 health potions
2. Go back when you reach level 6 and have your ult. Buy a catalyst and the first level of boots if you can. On your way back, grab the golem buff and try to gank your lane. This shouldn't be too hard even if they are at full health, just let your partner know and get to stunning.
3. Sorcerer's Shoes
4. Turn the catalyst into a rod of ages
5. Grab a sheen and eventually turn it into a lichbane
6. Zonya's ring
7. Most games don't make it this long but after this I usually have a hard time deciding what to get. You can grab a banshee's veil, Rylai's Scepter, or Deathfire Grasp. I personally like to grab a Rylai's Scepter for the added health and AP and the passive is somewhat useful too. I have never made it past a rylai's scepter before, even in the longest games I've played, but I suppose I would take a Deathfire Grasp.
The final item build should look like this;
1. Rod of Ages
2. Sorcerer's Shoes
3. Lichbane
4. Zonya's Ring
5. Rylai's Scepter
6. Deathfire Grasp
For runes I get magical penetration for marks and then for everything else I get AP per level. I've been thinking about getting cooldown reduction runes because it would be very useful to have the stun up more often but to me it isn't worth it. The golem buff helps give cooldown reduction, so I generally don't worry about it too much.
I'm not sure the exact levels to get Sion's skills but you should follow this basic idea;
For the first levels this is how you should get skills,
1. Start with enrage. I find that the added damage is nice for early team battles and the added hp for each kill is very important to an AP Sion.
2. Get Death's Caress next and use it to harass the other champs in your lanes. Be careful not to use it too often or you'll find yourself out of mana quickly.
3. Get stun next and use it together with death's caress to take out an enemy champ. At this point, if you have enough mana, a teamate with a slow or a stun could probably help you to take out an opposing champ in your lane. If you are solo, just bide your time and when you come back from getting the golem buff, you might be able to catch the opposing champ sleeping.
After levels 1-3, get death's caress every chance you can, stopping only to get your ult at level 6. After death's caress is maxed, get stun until it is maxed. It is important to point out that you should only grab one level of your ult until you are forced to choose between enrage and your ult. When this happens, grab a second level of your ult and then go on to max out your skills leaving enrage for last.
Summoner Spells;
Even after the nerf to cleanse, I still like to grab it. I believe it is essential to playing not only Sion but any champ in LoL. I've avoided countless ganks and certain deaths just by using cleanse. For your second spell you can grab whatever you prefer. I like to go with ghost but exhaust is pretty useful as well as flash which can be used to teleport to someone and detinate your shield. You could also grab teleport as you might find yourself going back to base many times do to mana issues. These would all be viable options.
Mastery;
I like to use an offensive based mastery build, making sure to get the magic penetration buff and the extra damage from the 21 point talent. I then go into utility and get mana regen, improved ghost, and put the final talent point into increased time for golem and lizard buffs.
Way to Play
The most successful way I find to use your skills is to throw on your shield and then pick a person to stun. Stun and attack them, and detinate your shield. Throw in another stun and if they aren't a tank they'll go down pretty quick. Most people don't expect this much damage to be done by a Sion and will come back for more many times before they learn their lesson. Sion is also very good at avoiding ganks, but it takes some thought from the player to realize what is going on. There were many times when a twitch tried to gank me only to die himself. If you are ganked, cleanse if there is a stun or a slow, throw on your shield and stun whoever it is trying to gank you. Throw on ghost if you don't think you can win and run to the nearest turret, otherwise you can try to take them down. Even if you do run, it is possible to kill them if they chase you too far. Explode your shield and stun them once again. This strategy will not work when there are multiple people so in that case just cleanse, ghost, shield, and run away. Throw a stun on one of them if they get too close. Often, a Master Yi will ult to catch me only to get stunned and watch me run away.
At the end of a game, it is possible to have 3k health, 2k mana, and over 400 AP, assuming that you have at least 4 out of the six items listed. Add in the golem buff and you can do some serious damage with little thought of mana.