This is my ryze build.

This runes help with early game dominance and helps late game.

This is just a standard mage mastery page. but if you feel you want the extra MP/5 regen instead of the 3% spell vamp (which isn't much anyways) then choose that.

These items help him be a tanky mage so he can deal out tons of damage and be sustainable at the same time. Also if you're laning against cait corki ect any AD finish frozen heart as quickly as possible, or if there's an AP mage in your lane and you feel they're raping you then get glacial shroud then negatron followed by an early force of nature.

This is what I use just for the fact that this will help with early game a lot and dealing a lot of damage with overload. Also when fighting someone do deal maximum damage do this Q W Q E Q R Q W Q E Q ignite. this WILL kill someone unless you die first. Or to lower their magic resist before you unleash full combo do this instead Q E Q W Q R Q E Q W Q

Now with these it really depends, if you feel you need to lane for as long as possible then get heal and teleport. but if you think you need more mana and no healing and need to lane long get teleport and clarity. exhaust and flash will of course always be able to get you a kill. Flash and ignite is just on the really offensive side, but ignite for sure, it will give ryze that extra push he needs early game to get early kills first blood ect.

Really try to poke with overload. ESPECIALLY after tear is gotten. you should have around 400-500 bonus mana by around 20-30 minutes if you're doing well, if not you'll have around 200-400. By your first recall you should be able to get tear AND tier one boots, if not have someone gank your lane so you can go back and do so. Also to secure a kill, act like nothing is happening, just farming minions and getting CS but then flash and Q W E Q ignite. that should take down about half their health. so at first they would be maybe here ______________ and it should be here by time that combo has set off _______. but always harass with Q until they're about here _______ then go for the kill. Q W E Q ignite for the kill. especially against an AD carry, i love seeing them overextend then flashing and doing Q W E Q and kill them because they underestimate the power of ryze.

Now, if you WANT you can gank but i recommend you just lane. but to do so you might want to use this combo W Q E Q R Q W E Q.

Pros:
Strong harass early game
tons of sustainability
tanky but extremely strong
can finish an initial burst but do it all over again in 2.1 seconds
Cons:
REALLY squishy early game.
AD carries tend to dominate pushing, can't push that well without being ganked by jungler(if there is one)
tends to get focused a lot.
Cannot push a tower by himself EFFECTIVELY.

You want to activate your ult then do this E Q W Q Q E. you can clear a minion wave with 10+ minions. make sure to claim a lane to farm late game if its being pushed unless someone has bloodthirster, then let them farm it. also last hit with your Q if with a well timed auto attack. basically what you want to do is before you get tear you want to last hit with well timed auto attacks. after tear use overload.

you want to stay at the back(of course) you want to focus one person with Q W Q E Q R Q W Q E Q if you do this the fisrt Q W Q E Q will most like drain their health massively. then the second Q W Q E Q after the ult is activated you should take some of the other enemys health. But you tend to get focused so be wary of that.

In all this guide will help you a lot, a score of 16/8/19 doesn't lie. can't screen shoot because i don't know how to post the picture.