Not Updated For Current Season
NOTE: I did not include masteries and runes because I want players of all levels and wealth (ip) to be able to use my build (:
Simply put, start off with spell flux, to level faster.
At level 2, put one in rune prison to keep you safe.
At level 3, put one in overload so when you get initiated, you can fight back.
After that, just follow these priorities.
#1 Desperate Power
#2 Spell Flux
#3 Rune Prison
Just get whichever ability going down this list is available first.
Ryze is a nuker, he is based on running and gunning or finishing other champions off. Teleport is used to save a falling turret or to suprise low hp champions by teleporting on a minion. Teleport>Ult>Flux>Prison>Overload>Dead
Ghost is helpful when you can't run away in time, when you get slowed or ganged. Ryze is a nuker. Don't try to shrug off the pain from a tank until you at least get your frozen heart. Reason? Cooldown.
Item Build Explanation
Start off with a soul stealer, you should play as a support for your team at the start of the game. You shouldn't die much and rack up some kills and assists, and the ability power adds up.
Next get some boots, depending on the map and enemy champions, boots of mobility is good for 5v5 and when the opposing has no stun or slow champs.
Boots of swiftness is also good overall, I recommend this as it helps more in combat. You could switch to boots of mobility later in the game when you get your frozen heart and glacial shard.
The rod of ages speaks for itself, most games should last at least 30 minutes. Getting the rod of ages mid game is great for Ryze. It builds up his hp to increase his survivability and also his damage, in the form of mp and ap. MP is very important to Ryze simply 'cause his overload depends heavily on both.
Late game, you should be expecting your overload to do at least 800 damage with a 2 second cooldown. >:)
NOTE: If you find late game your mp cannot keep up with your spell spam, consider an Archangels staff instead of the rod of ages. You get a barely noticeable decrease in ability damage but your mp should be able to keep up with the heavy spell spam this build relies on.
The frozen heart and glacial shard are great for their cool downs. Ryze is heavily dependent on the fact that he can snare others very often. His ult can also be easily taken advantage of. Both these items help your defense, raising your survivability and boosting your mp heavily, increasing damage and ability spam. By the time you get these two, your soulstealer should be almost done with its stacks. Adding onto these two items that is a total of 60% cooldown reduction! In battle, you should be able to spam spells without hesitation with help from arcane mastery. Your desperate power should have a cooldown of about 20 seconds and your Q,W,E skills should be able to be spammed in sequence without stopping. This is the highlight of the build. You will be able to shower enemies with spells while they are snared with only about 3-4 seconds of freedom in between. BUT, if you did this right, by 2-3 snares, any champion should be dead.
Your last items should be either Lich Bane or Zhonya's ring. You could choose either one as your end game item. They are both really good.
If for some reason the game is still going on and you have left over money, switch out your Glacial Shroud for the item you skipped previously, the Lich Bane or Zhonya's ring. You don't have to worry about the cooldown because the Lich Bane's passive ability pretty much turns your normal physical attack into a mini nuke from your insane AP.