Not Updated For Current Season
Before Game: When sitting at the shop waiting for the pre-game gank you should also pick up a health potion and a mana potion. This will help you stay out in the lane longer and allow you to go for a crucial gank or two depending on who your playing against.
Early Game: In the early game you should play somewhat aggresivly. This build relies on getting a decent amount of kills fairly early game. Now this should not be taken in the wrong way, if you get 1 to 3 kills with some ***its before level 10 you are right on track. Anything else is a bonus. Keeping this aggressive mindset in mind, you should probably try and lane with someone who has a snare or a stun to compliment your own awesome stun. Morgana, Veigar, Jax, or Xin Zhao are all incredibly effective laning partners. Targetting low health enemy champions (mages if in your lane) can help progress your build.
Mid Game: Hopefully by the time you reach level 8 or 9 you will have gotten at least zeal, but if you haven't don't worry. The best thing about Sion is that with each level up he becomes exponentially more effective. Mid game should be a fun time for a well fed Sion. With better than decent health progression and decent attack speed/dodge from your items and runes you should really start to feel the benefits of a long damaging stun and high crit. In my mind Sion with a lot of crit middle game is incredibly beneficial. So if you have the choice between a dagger and a cloak of agility always save for the cloak. Laning should hoepfully be over, but staying in a to push a tower or grabbing key jungle minions can be incredibly valuable to Sion staying ahead in the leveling.
Late Game: At this point any decent Sion using this build will have great damage, decent survivability and a lot to offer in a team fight. Things like Infinity Edge, Warmog's Armor and Liche Bane are nice, but late game items I think are entireably up to the situation. With a large amount of dodge and great health progression there should really be no need to get health or dodge, but once again if you are having problems with the enemy champions maybe some health would be helpful. Otherwise if you have raked up the kills earlier in the game you should be able to sit back and enjoy the crazy amount of crit damage you can do.
Overall: Sion is a well balanced and incredibly fun champion. His long stun combined with huge natural life steal skills and a damage resistant passive open almost any route to Sion. This build is meant to encourage team support and clutch kills, I myself have scored quad kills several times with this build. On the otherhand you will want to have a good feeling for sions abilities and be able to watch multiple targets health in order to maximize affectiveness. Have fun and good luck!