Not Updated For Current Season
This build is for a more experienced Sion, and I wouldn't recomend using it until you have a strong grasp of his abilities and statistical capabilities.
This build is a very powerful support/initiator. You'll use Sheen in combination with Death's Caress for lots of minion farming, and that will be the main source of your HP growth in early and mid game, so make sure you've gotten your last hits in. Early game it's all about killing minions and harassing enemies with Cryptic Gaze, although be careful not to deplete your mana too frequently. Mid game is mostly finishing your core and stacking Soulstealer, which you will do mostly through assists from CG initiation, DC nuking, or Cannibalism soaking. IMPORTANT: do NOT finish Lich Bane until you have more AP than physical damage when un-buffed - if you're having problems stacking Mejai's, then build some HP early (Warmog's works great) and drop Leviathan from your list. Late game, you'll be a strong player in teamfights, but you'll mostly want to be running ganks and not trying to tank. I've seen long games with Sion get up pretty high in HP, with plenty of defense from your masteries, but even with Cannibalism up you can get mobbed too easily because you don't have a huge amount of crowd control.
This game won't get tons of kills unless you're really good at picking off assassins and DPS, but your assists will be huge and it won't be too hard to stack both Mejai's and Leviathan past the return point. A very long game will even get you a few SotO stacks, but you could easily substitute it for Rylai's Soulstealer, Last Whisper, Bloodthirster, Force of Nature, or a Sunfire Cape.
In my experience with Sion, (he's the first character I ever played and my long-time main) he is far too balanced to specialize very well. His 1-to-1 AP nukes, damage reduction and Warmog-esque passives, and his massive DPS ult and Enrage passive mean any single traditional build will waste a lot of potential. This build is, in a way, highly specialized - it runs better than it fights, it engages better than it endures, and its damage output is good but not apocalyptic. However, it is very survivable and will make you a powerful player on any well-balanced team.