Greetings everyone. I have not been playing LoL very long, but I have played Dota and Demigods and know how to play these games. This is my first guide and it's all about the new Ryze.
First off. I have played a lot of characters and some of them were fun, but I never fell in love with any of them. I even played Ryze before the new patch and wasn't a fan. I don't like the useful once every 60 seconds play style of some of the characters.
Perhaps that is why I am doing so well with new Ryze...I never learned how to play with old Ryze so I don't have to unlearn anything. Unlearning is much much harder than learning. Well onto my Ryze build!

The runes are designed for maximum mana and 39.87 ability cooldown reduction after picking up glacial shroud.

Marks: Insight, nothing new needs to be said about magic/armor penetration. If you aren't using magic or armor penetration you are probably not using the right mark 9 times out of 10. Get 'em use 'em love 'em

Seals: At first I went with standard clarity runes. Then I had an epiphany. Ryze has such a ridiculous mana pool, (I've gotten 5500) the mana regen just isn't very useful while the knowlege runes give you additional staying power and extra damage. If you want maximum beginning power you can take flat mana runes but I don't recommend them.

Glyphs: Again, maximum mana is your friend, but 40% cool-down reduction is even more important. The 3 focus glyphs plus the 3 focus quints give you 6.87 cd reduction. Combine this with Ryze' natural 10% cd reduction and frozen heart and the 3% cd reduction mastery and you get 39.87... if you really really really want the minute .13 cd reduction and more early game reduction you can put a 4th glyph of focus. Also instead of mana you can put MR glyphs in if you feel like you need them, but because Ryze picks up so much hp/mp items he is rather tanky.

Quints: I chose cd reduction to get the 40% cd reduction. If you want to be more tanky you can get all CD reduction glyphs and 3 good old fort quints (I'm using fort quints myself at the moment) I believe the extra damage/staying power is optimal considering ryze gets so much hp by the end of the game.

I currently am going with the 9/7/14 build, but the 9/0/21 build is also good. With the 9/0/21 build you can drop a few cd reduction runes for extra mana/hp. I currently am 9/7/21 however. I can get over 60hp/5 which is pretty amazing, that with my ridiculous (4000 mana easy) mana pool you have amazing staying power. So basically it's your choice whether you want 1% extra move speed, extra cooldown reduction (which ryze doesn't need) and the summoner spell reduction, which is handy, but prefer the staying power of 40 or more hp/5. Either choice is fine.

Some people have pushed for the catalyst as your first combination. I have tried it, and I don't like it nearly as much as tear. Tear is clutch to Ryze' insane mana pool. Once you get the tear, cast spells constantly I would recommend getting a mana potion (you can get 1 health pot and 1 mana pot at the beginning of the game instead of 2 health pots) for extended spell casting. Once you get tear last hit creeps with overload for super fast farming. 2-3 regular hits and one overload will kill a melee creep and 1-2 regular hits and an overload will kill a mage creep. It is super easy to farm with overload spamming and you are also building tear mana. Make it a goal to hit that 1000 mana by 30 minutes. Always cast overload!
From there I recommend RoAges to quickly gain the mana/hp/ability power it provides. From there you can either get banshee's for maximum defense or glacial shroud/frozen tear for maximal damage. The archangel's staff will provide an amazing 150-200 ability power, so it's a nice finish, but realize that AP isn't very good on Ryze, but still a nice finish.
The 6th item Ryze gets I still haven't fully decided on. A RoAges would provide the most damage increase, but you will very very rarely ever have a game go on that long after you have already gotten the previous 5 items.
The deathfire grasp is another choice, and would seem great for any caster, but it is not so great for Ryze for a couple reasons. Firstly, Ryze is always casting, always, his overload is basically on a one second cooldown after full cd reduction. You will kill anything that doesn't have crazy high mana reduction in about 4 seconds. So another nuke isn't super helpful, but doesn't hurt.
Another choice is void staff if you are facing a ton of mana resistance. (remember though that the 15% mastery and the void staff will only give you 49% spell penetration.(Also remember Ryze's E lowers spell resistance(Also remember ability power sucks on Ryze)))
The 6th item is your choice but very very rarely will a game last that long, and remember you can get the banshee's earlier or later depending on how much you feel you need the spell resistance.

Skill Sequencing sets good Ryze's from bad Ryze's. I'm almost afraid of telling the whole world the secret to Ryze. Whats the big secret?
99% OF THE TIME, CAST OVERLOAD FIRST!!
IF you do this one thing your dps will skyrocket.
Let me explain. So alot of Ryze's I see will Rune prison followed by overload followed by spell flux. This is wrong wrong wrong! People are used to casters being useful once ever 40-50 seconds. This is wrong wrong wrong!
The correct spell sequence is q-w-q-e-q-repeat. For most interactions this will be how you deal sick sick damage very quickly. Your overload will be doing 700 damage easily pretty early in the game. Now with max CD it has about a 2 second cooldown. With Ryze's passive spam it CONSTANTLY. q-w-q-e-q... do that over and over again. It will feel weird at first because most casters don't have a spammable skill. Master the Ryze rotation and he will carry like noone else. If you aren't sure what to cast, cast your 800 damage 1 second cooldown nuke.
That being said, there are a couple times when you don't want to q first. If a enemy is almost dead and overloading won't kill him, and he is in range for rune prison, then obviously rune prison him. If you need to escape obviously rune prison.
Also, against tough creeps like baron and dragon you will want to q-e-q-w-q repeat because w will lower their resistance and cause your next q's to hurt even more.
Final point: use r as much as possible. This ultimate will (theoretically) have one of the shortest cooldowns in the game as long as you ABC Ryze (always be casting). Use it on large creep groups, use it on golems, use it on single targets. Use it constantly, it'll be up in about 15 seconds as long as you are constantly casting, and with your 4-5000 mana pool, you won't run out of mana any time soon. Also remember that r also counts for his passive cd reduction.

Currently I am using ghost and exhaust, but sometimes I use flash and exhaust. It is really just preference.
Sometimes flash will save your life where ghost won't, sometimes ghost will save your life where flash won't. Sometimes flash will get you the kill and sometimes ghost will. Both are good options(remember with flash you can pick up the 3.33% less death mastery(which is very ****py))
I prefer one mobility spell and one offensive spell, so while flash/ghost are great for mobility. Exhaust and ignite are both great offensive spells. However, exhaust can be used both offensively and defensively, and just like death fire grasp, Ryze will rarely be wanting for an extra nuke. Also ignite scales terribly while Exhaust is also awesome. If you choose ignite you can get the small critical chance boost in masteries.
Those 4 are your best choices.

Always focus on casting, and cast Q first 9 times out of 10, and watch your kills soar. Focus on mastering his spell order.
q-w-q-e-q repeat (start with R when you can. Don't let r just sit there. It has an amazingly short cooldown when ABCing.
Try to last hit every creep you can with overload to charge you tear. Try to get your tear fully charged by 40 minutes.