So, I've been playing Ryze for a while now and it's by far my favourite champion. Its a ranged nuker, with snare, strongest 1v1 burst and few real counters. Ryze is based on AP and CDR. He will need mana at first but by end-game it won't be a problem. The hardest characters for Ryze to fight are Silencers (Kassadin, Cho'Gath), bursters with stun (Anivia, feeded Pantheon) or anti-casters (Galio, Veigar). Aside from those, Ryze can defeat most champions one an even 1v1 match. If you get the element of surprise it will be even easier, since most squishy characters will die before they realize whats going on.

Q - OverLoad
Does damage according to AP and maximum mana.
Passive: CDR (10% @ rank5)

W - Rune Prison
Snare

E - Spell Flux
Bouncing Spell, 6 bounces long, reduces MRes

R - Desperate Power
BERSERK! Also makes spells deal AoE damage

Passive - Every time you cast a spell, reduces the CD by 1 second on all other spells

Ok, so Ryze needs CDR but you won't go for full CDR runes. You only need 6% CDR from runes, if you follow this build exactly.

So, my suggested runes:
RED - Magic Penetration - Always good to output some more damage
YELLOW - Mana/5 (Flat) - Always good to lane without having to worry constantly about mana
BLUE - CDR@18 - Buy them until you have 6% CDR at level 18 (OverLoad plus these will give you 16% CDR @ lvl18)
Mana/5 - The last 2 runes should be to help you with mana early game
QUINTS - Health (Flat) - Makes your character very less squishy early game and, since I don't buy Doran's Ring, helps with me not being targeted as much

9/0/21
You may change "Good Hands" in Utility.Tier1 to "Awareness" in Utility.Tier2 if you have lane partners or a team that can cover your *** easily. Since i usually go solo and most teams can't or won't cover me, i go for reduced dead time. The rest of the talents are pretty much standar BS. Having "Intelligence" and "Sorcery" gives you 9% CDR (added with OL and Runes, 25% CDR @ lvl18). "Expanded Mind" not only gives you mana but increases your OL damage, so it's a must :D

http://img696.imageshack.us/img696/4763/semttulovsv.png

Early Game: Start off with "Meki's Pendant". You will need the mana if you want to continuously keep harassing the enemy. Develop that into "Tear of the Goddess", so you max mana will start increasing. AT this point, buy "Kage's Lucky Pick" and "Boots" (i go for lvl1 boots only, but if you want to buy the lvl2 "MagicPen Boots" already, it's your choice). From "Kage's Lucky Pick", buy "Deathfire Grasp", the best item a Ryze can have. Enhances your burst damage so much that most characters will just run rom seeing you. Also, it's 15% CDR adding up to your current 25% from OL, Runes and Talents, will max out the CDR if your character at 40% (with is the CDR Cap).

Mid Game: From now on, it will depend on the other team. If they are leaving you alone and you want to go full out on damage, immediatly turn "Tear of the Goddess" into "Archangel's Staff". If they are targeting you instead of your partners, go for "Catalyst the Protector" and develop it into "Rod of Ages". After those two, go for "Rabadon's Deathcap" (if there happens to be a chance to buy the "Needlessly Large Rod" anytime in the game after you have "Deathfire", take it!). I buy the MagicPen Boots somewhere during this phase.

Late Game: At this point, you have around 500AP, can one-shot most enemies and terrify the entire enemy team. The latest items all depend on the enemy team. If they are targeting you in team fights, "Zhonya's Hourglass" is the answer. "Frozen Mirror" is also good against a melee team. "Abyssal Scepter" for enemy casters and "Void Staff" if they are stacking MagicRes. If you don't need any defensive items, just stack "Archangel's Staff" until you have 5 of them with "Rabadon's Deathcap" as a 6th item (over 1k AP!).

Ok, so the sequence changes from early game to end game.

Before DeathFire Grasp, rotation begins with Q (using R while it flies). If the target is isolated, use W on him, go near him (so that E bounces off you) and E + Q him (Q should be leaving CD by now). If the target is next to enemy minions or champs, use E first and then W, so he can't run/get near you. Q when possible and then repeat.

After Deathfire, rotation begins with R and then opening with DeathFire (deals 30% of target's CURRENT HP + 3.5% for each 100AP you have). AFter that first big hit, Q and then E or W; depending on situation mentioned above.

When fighting a Tank with MagicRes, opening with E to lower MagicRes is recomended.

I prefer using Ghost and Exhaust. Both good to chase or run from enemies, they are completely my style. Flash is also a great spell (entering brush, flashing to next brush and surprising the enemy is just exhilarating), also useful to run. Clarity is good if you have mana issues, Heal is good if you get targeted a lot, Teleport for quick defending and the others aren't that good.

You are good with any lane partners that can keep people off you, like Taunters (Shen is ****ing great, can save you with ulti and taunt them off you), Snarers (Morgana, combining her snare with yours and her Spell Imunity is great for early kills), Stunners (once more, they stun and you kill) and general pushers and CCers (Singed is great to pull them off you, even is he doesn't have Taunts).

The bad partners for you are Tanks that can't save you (when running with Mundo, i always get targeted and there's not much he can do to save my ***) and stealthies (running with Akali, you already had a high chance of getting targeted. When she becomes invisibles, that high chance turns to 100%!)

When you are against a team that knows they must nuke you first, you need to make sure your team can cover you while you kill, because a Ryze can't survive a nuke for longer than 2 seconds...