Alright forgive me if this is not standard and some don't like this. This personally is my favorite way to play Ryze. I will go more in depth in the areas and show you how and why I picked what I did, I hope you will see why and use this as well :)

My MPen marks are because the magic resist people build hurts him badly and this plus the 15 from boots, and the 10% from masteries stack well and penetrate tons of the MR.

My HpL Seals are for sustainability, Ryze starts out with roughly 445 hp and the health per level help, at level one you start with like 456 or so.

My MpL Glyphs are for damage at level 18. Ryze's absolute main damage source is his mana. His Overload benefits heavy from it along with Rune Prison.

My movement Quints are because the harass early game and move-ability end game is very useful to run around the lane.

21/0/9
These masteries are used for almost every ability power champion so they are pretty standard.
The reason you grab both the specialization in Ignite and Flash is for the increased AP from ignite even though it isn't that much, and the decrease in the CD on Flash.

My items may be a little controversial but they are definitively the best items possible on ryze.

1st: You must always start Mana Crystal 2 pots, you can do boots 3 but its not as much damage output and you will have mana issues.
2nd: Tear is the first item you build, stack it up for later when you make AA since the stacks carry over.
3rd: You can get Catalyst or Shroud doesn't matter but Cata is better first in my opinion.
4th: Full boots and shroud are necessary.
5th: This is where things just go situational, You can build a second catalyst if your having no issues(i know the passive didoes stack but its for hp and mana), or if your having issues based on your lane or other fed people pick up a frozen heart or banshees for the resists.
6th: You can build RoA earlier or later I build mine later because the resists help early and end.