Ryze can be an *extremely* effective champion in any type of game. The problem is, most people have no clue how to build him. Instead of using AP, he benefits more from stacking mana due to it increasing his ability damage by 8%. Hope you enjoy.
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First I like to grab some health potions and a mana crystal, mainly because it helps you stay in your lane longer so you dont have to go back as much. After that the guide pretty much explains itself, the reason you stack mana as Ryze (For you Ryze newbz)is because his spells do more damage based on 8% of Ryzes mana pool. Which is a very unique trait that he has.

There are a few effective ways to structure your summoner spells based on what type of game you plan on playing. The first one, is if you want to play more offensively; Ignite/Exhaust. The second is if you want to play more defensively; Flash/Exhaust. The third and last most effective spell to use is somewhat a hybrid; Flash/Ignite. It helps you pick people off if they are very low, and also helps getting away if you are being ganked or stunlocked.

For the most part, Ryze is effective in team fights because of his ulti, and 1v1's just because he is (:. If in a team fight, Pop your ultimate, use spell flux, rune prison, overload, and then just rinse and repeat.
For 1v1's, Start with overload, then rune lock and overload, and keep repeating this until your enemy retreats or dies (2nd being the most likely). Sometimes you might want to start off with a rune lock if you have someone near you that is ready to gank, just to keep em' still so your team mate can do some damage to them as well before you have to give chase. Once again, it just really depends on your situation, but once you get used to Ryze you will understand what to do in what situation by heart.
Disclaimer: **((DO NOT FORGET TO WEAVE AUTO ATTACKS BETWEEN YOUR OVERLOAD AND SPELL FLUX))*

-Begining game, Ryze completely destroys. He will be getting kill feeds and the like if played correctly (and hoping your team is decent and the oppossing team isn't.)
-Mid game he lacks a bit unless he was fed in the beginning. This is just because he doesnt have a ginormous mana pool yet so he cant quite nuke people yet. But, if you are fed you can dominate people thee entire game without any problems unless you go all suicidal and play too offensively. Most of your kills will come off of melee and casters moving into your range.
-End game is when Ryze starts to weaken a little against tanks, and melee DPS but against casters and the like he can still beat down without much difficulty. However, you have to be a bit more cautious at this point because people will realize how hard you can nuke them if you aren't taken down quickly.

-Farming can be nice with Ryze just because he is so much better after he obtains all of his items. If possible, (and depending on team comp.) try to take the solo lane in 3v3 and mid in 5v5. Take as little damage as you can begining game, if you are overwhelmed mid-game don't feel hesitant to pop your ulti and nuke all of the creeps as it can give a nice money feed and help you push. If not possible to take the solo lane, try to organize ganks and get some more gold that way. Trust me, the faster you can get all of these items the harder and faster you can GG it.