Don't stand near marked minions as Ryze can spread his
(Spell Flux) on you and then poke you with an empowered
Ryze uses a lot of mana in the early game if he has to match a pushing wave. You can push him in to make him burn through his mana and have to back. Or, he will be unable to trade with you while gaining whatever farm he can.
Try to fight as often as possible. Ryze needs time to scale, so delaying his ability to scale is key. Try to fight him as much as possible: preferably after he wastes an ability.
Ryze is late game champion. Try to beat him in the early and mid game when he is vulnerable and put him behind so he is unable to scale.
His team fighting is similar to that of an ADC except for the fact that he is more tanky thanks to his itemization. Try to focus him down first in a team fight so he is unable to burst anyone down.
As a tank, try to cover your team by standing in the frontline and in front of Ryze so he is unable to burst down your carries with an
combo. As a carry, try to hide behind your frontline.
Take care for his level 3 when he has all of his basic abilities as he can deal a lot of damage. Although his main combo does eat through a lot of his mana. Poke him down and stay out of range of his marked minions.
At level 14, he has multiple points in his main damage abilities. Make sure you invest in magic resistance if he is ahead.
Ryze scales with AP and mana, so his damage rises at every level and every item he gains. He has no real power spike, his damage just rises constantly. Do not let him scale by either shutting him down or finishing the game early.