Ryze combo?

E (if in minions) w q-q-q-e-w q-q-q-q-e-w spam w whenever its a clear shot for your w, e is targeted so it dont matter

The passive reduces the cooldown of your skills depending on your Q cooldown and has a minimum of 0.25 seconds or something. So when I play Ryze I go like this (with 4 charges); Q to trigger passive, W, Q again as the cooldown is refreshed, E, Q, W, Q, E, Q, W, Q, E ...... So you basically spam your W and E skills while adding a Q between them as it will most likely be off cooldown all the time. Add your R somewhere in there and you are good to go. Also, I am pretty sure you can't do it fast enough to keep the target perma-rooted (there is a very very small pause between the roots) so consider walking closer while using the combo to prevent them from escaping at all.

The Ryze combo is very similar to the Katarina combo.

You start with your left cheek pressed against your keyboard, and then roll to the right. Be careful when you roll to not accidentally hit alt and f4 at the same time (that's actually the counterplay, good opponents will get lucky and you will disconnect shortly though sometimes even this won't stop you from killing them).