AD Ryze is a great way to play this champ, but it`s also a bit difficult, especially at the begging, since he is a bit squishy. As build progresses, your chance to survive will increase, due to raising the amount of HP and armor. At the end, your Ryze should be probably one of the best champs in your team. There are few things that are explained bellow, that should greatly help you succeed in this build, but I won`t get into (by my opinion) unimportant things, keeping it short.

Well there are few important things to mention about this build.
As the first If you start against a pest enemy team, you should first get the Catalyst, and primarily focus on building Rod of Ages followed by Frozen Hearth.
As the second thing YOU MUST HAVE HEALING POTIONS ALL THE TIME. Well at least until you get your Will of Ancients, which should have the same effect.
And as the third important thing: HIT AFTER USING ABILITY TO ENSURE MAX DAMAGE, especially when you get Lich Bane.

I RECOMMEND using Clarity because this champion is very mana thirsty at the begging, and especialy when playing 3v3.
Flash - is pretty self-explanatory.
Teleport - is my second choice, since Ryze is mage (as almost every mage SLOWER THAN YOUR MOM ON EXERCISE BICYCLE), because sometimes you need greater mobility and I recommend taking it instead of Flash.
Ignite - is also useful when playing in this build, and is also self-explanatory.
Heal & Cleanse - yes, you can take these 2 if you just can`t handle being harassed. (Noobs...)

Well that was my short guide to awesomeness, using Ryze, I hope you like it, as small as it is (still taller than RWJ), and don`t forget to rate and comment it, thanks and see ya :)