A common AP build for most of you that play with ryze.
He's a easy champion to master as long as you respect one thing ... don't get greedy !!!
Ok first things first why AP build and not mana or hp build ?
To answer that i'll just say that AP build for me it's the strongest of them all (not the one that will give you best survivability) but certainly one of the most efficient on ganking, most of the times, with a m8 or alone.
As many have described, ryze is a glass canon (due to is high dmg/low HP relation) the truth is, yes you can kill very well on 1-on-1 situations although, that wont happen alot during mid/late game were the team usually gathers to gank more efficiently.
Truly,you are best killing light melee champs or casters coz if you try to kill a tank it will be hard !!!
You can't kill a tank alone unless a) he's not full HP or b)you are in late game and have ALOT AP, and even then be careful !!! Try to solo golems for auras from lvl 9 or so (it will improve you money account and give you nice buffs to kill better).
This build will provide you with a good kick right from the start and with luck (or a good partner) start ganking early game !!!
The AP will make you're spells really powerful compared with the majority of the other casters and the magic penetration will make them sting as hell !!!
If you go with top or bottom lane try to hide in grass as fast as you can and as soon as the first enemy comes close to the grass use spell flux (it will bounce on you) and will take half HP of any champ almost every time (it will scare the **** out of them ^^)
Just a little something before i get into the game play.
My skill build can be adjusted to better suite the champs you are facing on the lane but 80% of the times i feel this build is the most efficient.
You'll start with the best harassment spell and also one of the most powerful spells from ryze (spell flux) so you can keep them in check wile getting minions to lvl a bit.
The rune prison to make them stay to take more damage from spell flux.
For me learning just a lvl of overload is enough for early game as the other spell are way more efficient to gank/kill other champs (spell flux) and to keep you safe (rune prison).
But this is just my point of view and the following description is a sketch of the majority of my games (it's not 100% what will happen but you want it to be close to successfully use this build)
Start with buying amplifying tomb with an health pot and you'll be fine till lvl 5/6, time when you'll have just enough for 2 things (take the tomb and make a mejai's soulstealer and the boots of mobility).
Side note here just to justify the why i make the boots of mobility and not the sorcerer's shoos.
As many of you know the magical penetration you get from the rune build and the mastery build will be enough till you get the void staff mid game, and also the speed the boots of mobility provide, is a bigger advantage either to run away fast or to gank some low life champ alone in a lane (for me it's important to be able to do both, as you will majorly be on the back of your minions rushing to the enemy champs to gank, or running away from a possible death scenario - avoiding lose the mejai's bonus).
Try to gank as much as you can remembering the one rule wile playing with ryze (don't get greedy).
You are squishy and other champs know that ... so you'll be the first target almost 80/90% of the times during a game wile in a group run.
If you run alone you get killed easily or if you get to greedy and run after a low hp champ alone you will probably have the same fate (as you most likely will be ganked by they're team mates quick !!!)
Learn your place, be patient and look for good opportunitys to kill.
Latter on (looking into mid game) you will have some death on your mejai's and enough money to get at least sheen and a blasting wand (item's needed for litch bane) if you have the chance to get them, do a quick return and buy them, as they will help you gank better and filling the mejai's a bit more (bring you the profit needed to finish leach bane and more AP).
As soon as you have enough it's time to get void staff as it will provide you a good kick on AP and +40% magical penetration making other champs less resistant to your spells = more kills/money (you can see a pattern here don't you ?! ^^).
Usually the game end's here (you with the above item list and 2K money to spend) but if you still haven't done the job it's time for the big finally were the Zhonya's ring will shine like no other !!!
Start buying the blasting wands and as soon as you have the money for it just buy the damn thing and finish the game already !!! (you will have close to 600 AP or more depending on the state of you're mejai's buff) and with your ultimate well ... you can see the damage can't you :P
That's basically it !!!
The summoner spells may vary with your preferences or game style ... clarity is a must for early mana boost and better ganking/harassment, as for the heal well, as you know your life is not that good and in a tight situation it can make the difference between getting to the tower and teleport back to heal or dieing :S Although it's a bit bad late game (i admit that) can easily be changed to teleport or (peoples most picked option) flash. Either way good options !!!
Thanks for reading this big wall of text *sigh* and hope you like this little "guide" !!!
If any doubt or critic you can comment here or add me in game (Deathmark) ...