Ryze is a mana dependent DPS NERF champion . With this build you have both mana and ability power.

Those are Athene's runes . He goes for magic penetration from runes which with boots gives him the 30 magic pen which basically counter every champion's basic magic resist . I go for spellvamp because its 6%(runes) + 3%(masteries) = 9% spellvamp at lv 1 . 9% + 25%(ultimate) = 34% spellvamp at level 18 without any other spellvamp item .

Your Q will be your main damage ability so you will max it first and harass your enemy . You can either max W or E second but i prefer maxing E .
Your E deals much more damage than W and it reduces MAGIC RESIST which is very important . But , if you wanna be sure you kill your opponent when your jungler ganks you , max W for increased root duration . Your burst should be : (Activate Muramana) Desperate Power Overload Rune Prison Spell Flux Overload

Pros : If fed , 2 ghadd dayumm overpowered
Tons of damage
Your Q can be spammed , you have only like 2 seconds cool down
Your AoE damage Desperate Power is very good for farming and very usefull in team fights.
Immense range on your spells (675 , 625)

Cons : No escape ability
With BLUE BUILD (which is the best) kinda squishy.

As you get your tear , spam Q , W , E on minions so you stack it . Harass your enemy with Overload Rune Prison Spell Flux Overload WOMBO COMBO NIGGA . When the jungler helps the enemy push your lane activate your Desperate Power and Overload Rune Prison Spell Flux Overload the minions so they won't be able to push without minions.