i'm not english and i dont know it very well, but one think i know it's how to play ryze...

I pick that item on that guide, but how all people that know the game, every match is different from an other...so basically u need to take someting like that.

Very important to dont forget are a few thing!

1) Mana! if the item dont give it, or u are on late game or u really need it.
Ex. If the other team have 3 ad or the enemy ad is really feeded u have to take thornmail and maybe before the glacial!

2) Survive! u are the first target expecially on early game, so u need resist. Magic resist and armor, not so much life cause is useless at early game if u have not resist.

3) Cooldown reduction! u need it, like a 20% and normally the blue rune is your so also if u have only the glacial ( 15% ) with blue rune u have no problem in fight!

4) why not ap item? ap is good for your snare (but also mana works) and for the spell flux, but how u can see spell flux isnt too effective on early game and if u take ap only for one skill u are going to fail!

This is not really easy.
I never seen an skilled ryze except ATHENE!...but he is not a good ryze, he has find a way to use it! Ryze is like an very very very powerfull bomb with a code, if u know it no way for enemys but if u don't u can use is only to /d!

Just start with first skill, and do last hit on minion. And when u see that the enemy is going little bit near ur range u go againt him and press Q!

when him has 35 - 40% of life u can kill them at lv 3..or before if he ia a nub...sometime happens on hight ranked level..i dont know how, but!....

u have to know that at same farm, minion, kill, lv..Ryze do more dmg! so play aggressive is the way!

if he escape, dont care about it...u gain more minion so more farm so u can dominate the lane! just dont die or u are going to lose the tower cause ryze have to farm lv and minion without die! Remember that is better 0 kill and 0 death that 1 kill and 1 death.

an other way to play, if u cant kill or shall him on base u can play very but very passive, till the jungler comes.

to play passive u need to stay far from enemy and use skill to his minion not only for last hit but to kill them....that permit u to play safely till gank!

Your standard Burst combo is:

Overload -> Desperate Power -> Spell Flux -> Overload -> Rune Prison -> Overload

Your standard sustained damage combo is (Great for Blue buff and fights where you don't think you'll need burst, thanks so much for the suggestion FighterRanger):

Overload-> Spell Flux-> Overload-> Rune Prison-> Overload-> Desperate Power-> Overload-> Spell Flux-> Overload-> Rune Prison-> Overload

You should be able to get the first combo off extremely fast, since casting two spells after Overload reduces it's cooldown by 2 seconds thank's to Ryze's Passive, making it a 0.1 second cooldown with 40% CDR. The second combo gives a much higher sustained damage.

For that reason I highly recommend you use smart casting (Think Karthus's Q). Smart casting allows you to cast while just hovering your mouse over the target. Essentially cutting out the "who do you want to target" phase. Some consider it an acquired taste and you'll probably need some time to get used to it but I with out a doubt think it will make you better.
Enabling it is as simple as going into keybind options and rebinding your Q, W, E, R to the Smart cast version. (For which the default is I believe Shift-Q, Shift-W, etc.)


Why Spell Flux before Rune Prison?
Because it lowers magic resistance. Nothing major. This doesn't apply to the second combo because you are spreading it over a few seconds and they aren't just going to sit down and take it so you need them to stay put.

I HAVE TAKE THAT PIECE OF MY BUILD FROM A " Ryze revamped, AP be damned. "
just cause i would say the same think...the guide before explain really better than me how to play it..but i think sonothing different from him^^