I don't really feel like writing a Ryze guide, but I do feel like sharing my opinion on him with Guides & Strategy. I've been doing it slightly different from a lot of people I've seen, so I figure it may cause some interesting replies.
* Sorcerer's Shoes and Chalice of Harmony, in the opposing order, have pretty much been the one thing I've gotten every time. I find I never need more then Chalice to keep my mana under control. Since his ult is FREE, sometimes you only need as much mana as to cast your Spell Flux to get a kill. Sorcerer's Shoes on the other hand, I'm not so sure about. I'm starting to get under the impression that Ryze benefits from having a quick move speed.
* Most important stats, in no particular heirarchy: AP, MP, HP, Resistances, Magic Penetration. Now I've had people go mad and froth at the mouth with me that I'm not prioritizing Archangel's and -CD Reduction. To hell with that.
* Kinda solo lane reliant, pretty slow early game. Ryze is slow to rise. You'll be playing catch up with carries, you won't have the one great item that will suddenly make you godly. If you can get kills before the 10 minute mark, that's lovely, but you have to play like you can't count on that.
- Ryze's Passive gives him stupid amazing -CD Reduc already, why shave off fractions of a second here and there?
- Ryze with even more -CD Reduc is Ryze with even less mana. With only a mastery's worth of -CD Reduc, I can be totally mana efficent with Chalice. Once I start stacking on extra -CD Reduc, my mana pool starts to drop and I'm forced to re-itemize my sustainability.
- Bursts of amazing damage are better then being able to spam abilities up a lane. Sure, fast casting Ryze is a lot of fun, but when the **** goes down, I like to put myself into situations where I only have to launch my spells once.
Ryze can get around this by soloing, which isn't really that hard. If you could get your hands on a solo lane for a couple minutes here and there, that really benefits you in the long term. A gank happy lane partner in a safe and comfortable lane? Great for Ryze. Somebody who disappears to jungle every so often? Great for Ryze. Of course, you could be the mid solo, or your team could have a jungler, which means two solos.
* Spell Flux, Rune Prison, Overload. In that order. Rune Prison has been amazingly underrated since the change, and it's more important that your Spell Flux do all it's damage then Overload do any at all. Plus, a cheap 50 mana Overload is great for last hitting minions and lowering all of your cooldowns via Ryze's passive.
* Teleport and Ignite. Specced Ignite will make up for your lack of early game, and Teleport will help your lack of mobility and health regen.
- Getting Spell Flux stuck between two enemy champions deals the most damage, especially when you have Desperate Power on. That way each of them takes full damage per bounce in addition to 65% on off bounces.
- Don't be afraid to farm with Desperate Power. It's FREE, and you'll get it back quick. Plus, you need all the money you can get.
- Spam your cheapest ability when Desperate Power or Rune Prison are down and you see yourself needing them soon. If Desperate Power is up, conserve your mana.
* Abyssal Scepter. 'Nuff said.