this is not my guide. im just reposting it here. credits to Lendari
Ryze is very straightforward to build and to play. He is the most powerful direct burst damage dealer except maybe for Evelyn. He's pretty vulnerable in general, but when played right he is very difficult to solo gank because he can kill the ganker first.
Anything that reduces cooldowns or increases AP. HP\Mana regen after that.
1 - AP boots
2 - Lich Bane
3 - Archangels Staff
4 - Zonya's Ring
At some point you may want to get a HP regen item... particularly if you're solo vs. two but Ryze can't creep or jungle well so saving money is important. Don't buy it straight out.
Choose the skill with the lowest number that is available at the time of level up.
1 - Ultimate
2 - Rune Prison
3 - Lightning bolt
4 - The W skill
This means early on you're maxing rune prison (and a little bolt), mid game you're maxing bolt and late game your building the AP to damage skill and your ult is always maxed for your level.
You want to take survivability skills. Definitely take Boost and then you can take either Exhaust if they have a lot of melee or Flash if they have a lot of casters.
Early Game + Defending Solo:
Always maximize your AP at any given time. A low AP Ryze will not be able to do any meaningful damage, almost ALL your damage is gained through AP. The level 1 of your bolt does 20 damage + AP. Getting the AP boots will double your early damage. Build new items (like lich bane) by spending on the prerequisite items with AP first (books and rods) and then getting the rest or the prerequisites.
Save your rune prison until someone walks into range. Cast it and then stand there and attack them. Throw your bolt before they run away.
Rune prison someone at the base of a tower right after they attack you and the tower focuses on them...
Never stay in a vulnerable position while rune prison is in cool down and you're not doing any damage to someone.
Use rune prison to punish anyone who tries to get close to you or chase you.
Rune prison, rune prison, rune prison. It's the only good skill you have until you get substantial amounts of AP. The ultimate is also useful early game.
Ryze cant creep or jungle until he is building the AP to damage skill (late game) so gold is always limited for him. Ask your team for a solo lane!
Ryze's ultimate cools down relatively fast. People will tell you you're stupid - but don't ever be afraid to use it, even 1:1 it's not a waste and it will be back really quick. Just use it all the time IMO.
EXCEPTION: Never use your ultimate when you are around a lot of creeps. It's a complete waste of bounces if it bounces between the creeps (and it will).
EXCEPTION: Never cast it and run away. If you're not in a position to stand still or chase, don't use the ultimate.
The most effective use of the ultimate is to let it bounce back and forth between two enemies. Ryze is very good at getting double kills like this.
It is also (slightly less) effective to let it bounce back and forth between you and one other person. Anyone who attacks Ryze solo to gank should be punished in this way, (especially Yi, Ashe, Annie, etc...) it's a guaranteed kill for pretty much any caster or DPS character and it will do enough damage to make a tank run away and be highly susceptible to a kill from your bolt or teammate if your AP is high enough.
You can move around while it's out... and you should move towards them. If the person is running away, you need to follow them and the ultimate will keep bouncing through you back to them while you follow.
Attacking as a Team:
Stay in the back. You'll be dead in a second if you get thrown or hit by a strong spell. Boost is your friend.
Save your rune prison until someone on the other team over extends into your range, if there is an Alistar or Singed on your team wait for them to throw someone then prison them. Basically use RP to set up your teammates for an easy kill and to stop runners.
Ryze's ultimate is one of the best ways to soften up a large group for your teammates (this might be the one attack situation where you DON'T lead with rune prison because you want to trap someone who stays behind when they run back). Starting a 5v5 fight with an ultimate will usually cause enough chaos to put the other team on defense and let your team break their formation. Obviously all the other rules about the ultimate apply here.
Always be the first one to go back. 10\10 times Ryze will die first.
(optional) Try not to constantly killsteal your teammates.