I saddens me to read that people say "nobody plays Ryze anymore" and whenever I see one I understand why. Very few people know how to play Ryze. The keys are max CDR as fast as you can, changing your keybindings to smart keys, and the correct skill order. If you do it right he will be able to fire CONSTANTLY with insane damage very early in the game.

Before even considering playing Ryze:
#1 Put on smart keys in keybindings, so you can shoot without pressing the mouse button. Just do it, you'll see. Learn how to fire your spells while running closer to enemies, maybe after a stun.
#2 Use Q every other spell, usually QWQEQRQWQEQ is the best skill order. Until you get glacial shroud you might want to go QWEQRQ.
#3 The first 3 items are key and should always be built first. They will give you 1800 bonus mana, almost max CDR and magic penetration for around 3600 gold as well as hp, armor +++
#4 Scream and cry till you get mid, then learn how to use blink to take down that fool down or make him flee so you can go buy your tear. Try to save mana for your opponent until you get your tear.

Now as you see you're passive 1 second CDR on cast is what makes ryze. With max CDR his Q is 2.1 seconds. Once you get that Glacial shroud (15%) and lvl 9 Q (10%) + Runes (5,85%) + masteries (6%) = 36,85% which is enough to get you casting your Q once every second. With around 200 close-to-true bonus damage + 150 base at lvl 9. From Q alone. Yeah. I havn't listed the full build because you have to be flexible.

Even if you can't kill anyone just stand mid and keep lasthitting creeps. Stick to your Q and in 10 minutes time your tear should be near fully charged and you'll have ****loads of gold anyways. If you don't get mid that sucks but you can still own, it all depends on your partner.

Adapt these as you'd like, this is my preferance. Magic penetraion marks should be obvious.
For seals I prefer armor as it will give you much needed survivability early game, but mana regen or max mana at lvl 18 runes are also viable. Glyphs of focus is my choice, some go for the scaling ones, which are better after lvl 13 and cheaper, but you want to get that CDR asap as it is your main strength. Swiftness quints along with utility build will make you able to chase and get away.

Max utility build is a must. Too many important bonuses to pass up. Expanded mind is unfortunately based on base mana so it's no good. The choice lies with defensive or offensive mastery for the last 9 points. I've tried offensive, which lets you get 39,85 CDR with glacial shroud, and 15% penetration (after reduction) but I've found the extra survivability and the insane health regen of defensive mastery to be more valueable. Feel free to try both.

A lot of my kills come from offensive use of blink and ghost, but ignite is also viable instead of ghost for early mid domination. Sometimes even Ryze has to run tho so you can use it for too I guess.

I just put this out, so please don't downrate it because you think it's short, I'll try to write more a bit later and maybe put out some videos of teamfights and early mid.
Well have fun, go press QQQQWWWQQQEEEQQRRRQQWWWQQEEEQQRRR while you're screaming and laughing. Crush your enemies, see them driven before you, and hear the lamentation of their women.