Ryze is not a tipical mage, he is a kind tanky. Because all his skills take mana to do dmg, you have lots of mana and lots of dmg. The passive helps you to reduce the cooldowns. So you can stack 6 items with def and mana.

I took overload for the first skill because of the low mana cost and you have the passive of the first skill which helps you reduce cooldowns. Then you take cage to make enemies stand on the ground and bounce(spell flux) which helps you do aoe dmg or more dmg to 1 enemy.

I took ghost and flash. Because the only think he needs is speed. So you need clarity or lets say ignite. You just need movement and nobody can harm you.

Ryze is a good late game mage. So if you buy him tank/mana items nobody can kill you. So all you need is to nuke the enemies with spells. If they have a shield, lets say for spell blocks
(banshee`s veil) use overload. So you use the lowest mana skill. But if you are stunned you are dead, so keep melee champs away from you with cage.

Always use the cage when the enemy runs away, so you carries can finish him or her off. Cage the melee carry so(no dmg of him/her). Focus on low hp champs or carries. This is all for my Ryze spec hope you enjoy and like it. BB