When laning as Ryze you want to play passive and last hit (obviously). Once you hit Level four you can be a lot more aggressive. Use your snare (w) to set up ganks and secure kills.

Remember Ryze is a unique champion his skills also scale with a mana so you have a huge advantage over ap carries that need mana in the early game. That is why you want to rush tear of the goddess and catalyst the protector. If you feel it is necessary you can get a banshees veil to be more tanky.