Aight, i will try to give you just a full on guide on how to Play, Build and utilize ryze. for any questions feel free to comment.
Alright, as for what you can do with him, you saw the comments below for his gameplay combos.
For Runes, take 6x Scaling CD blues and 3x scaling or flat mr blues, 9x Magic pen reds, 9x scaling hp yellows and 3x movement speed quints
Masteries can vary, depending on your matchup. Most favourable masteries on ryze have been 12/18/0 assassin Build up with stormraiders surge, or you can go for the mages 12/18/0 with thunderlords.
Summoners are strongly player-taste depending. I personally go
for better lane pressure early to return faster after i get my tear, my catalyst etc. Most people however will tell you to go
, and for good reason. Ghost's synergy with stormraiders is nuts lategame.
NEVER take
. On ryze you have too Little quick time damage early on to compliment it and will therefore always have yourself fukd. Ryze earlygame cannot all out efficiently due to manacosts.
As for his Itemization. take
and 3x 
Rush a
and
and, if you got that much gold or managed to stay in lane long enough, the starting components for 
Your Core Items are ((In chronologic order of completion))

Offensive item choices for you are

Defensive items would be:

Items to NEVER Build on ryze:

As for his Skills, Start with his E, Spell flux and try to last hit minions with it so you spread flux for a lot of lanepressure early, threatening your enemy from any csing.
Skill Maxing, in this order, i persoally prefer:
E-Q-W-Q-Q-E-E-E-E-R-R-Q-Q-Q-W-W-W-W
Basically you start out normally, put a point in E Spell Flux at lvl 1, Overload at Level 2 and Rune Prison at Level 3, then until you hit 6 You go by standart maxing, Q first. When you hit 6, I personally start growing into a waveclear bot by maxing E first.
You can put a point in R and go on with the typical maxing order to go Q first, but it is highly not recommended. Reason for that is, ryze's Ultimate like most others offers close to nothing for solo actions early. You can do nothing with it and the range at Skill Level 1 is so incoherently short that ganking is flat out impossible if the enemy has warded well enough.
So instead reapply your focus on your own lane. compensate the lack of kill pressure by being an inpassable wall that blocks enemy pushing. Ryze is a very strong character for split pushing and possibly one of the only mages ingame who can splitpush at all due to his unreal waveclear.
at lvl 10 and 11, unless you are drop dead behind, you will enter the central stage of the midgame where your power starts coming from your items and not from your skills, meaning that you can then proceed to max your ultimate out since it will make close to no difference to your gameplay style.
After Level 11 proceed with the standart max of Q and then W lastly.
Teamfights are gonna be a difficult aspect. You will Need to try and flank the enemies and try to spread spellflux as wide as you can. Try having the team cuddle close together and apply Spell flux on the tank then spellflux him again to spread it through the whole enemy team then Q into them. Save rune prison as either a distortion tool or as an failsafe for escapes. It is your only utility and defence you got.
Note that ryze's Ultimate also transports allied Minions, so maybe try cheesing a push by teleporting a massive minion wave straight into a Tower.
Or for some fun Plays teleport a minion horde into fountain. Fountain is not coded like Towers and will therefore not focus you should you attack anyone. It is coded to attack in the order of who enters it, so you will have a lot of safe Play to quite literally siege their fountain for some brutality.
Last but not least:
AVOID UNWARDED BUSHES!!! Ryze's Kit is very heavily focused on point& Click and his ranges are not all that big. Walking into unwarded corners and bushes is lethal for you more than for most other champions, since you will have a lot less effective means to react. Ryze is brutally weak to traps and ambushes.
As for Positive Matchups i go with

Because you can Flux his Turrets from safe ranges. Just beware his stun bombs.
Because you can just Rune Prison him and walk away from his engages, plus your trade's are stronger as the game go on. Just beware his lvl 2 cheese.
Because she has roughly the same ranges as you but is a lot less proreactive as you are. You can with all your movement speed literally run circles around her W while dodging it, and possess roughly the same trading power but a lot stronger burst lategame.
Because he is a very stationary and slow champion. Easy target to walk around and kill, just be careful of his R Requiem
Equal/Skill matchups are:

Because a good ahri can play around your Rune prison with her Spirit rush if she uses it fast enough and if she gets close enough. Unlike you, her main damage Tools ignores minions, making her Poke inlane a lot more reliable than yours. But you possess a lot more versatility infight and your shield can save your life if you can proc it
Because his ranges may not be as big as you but by god are you and Azir the same Kind of annoying lanepressure guy. He with his soldiers can do the same Thing you do with your Spell flux, zone you from waveclearing. Plus his Shuriman Shuffle is dangerous to you if he gets a gank. But azir lacks your solo potential early, which he makes up with a lot more forgiving manacosts.
and Ryze have kind of the same style of gameplay. THis Positionheavy speedy as all hell Hypercarry-Mage hybrid with burst out the ass. Cass has bigger ranges than you, but is less forgiven on mistakes. Stormraiders against her is highly advised to negate the slow on her Miasma.
Kassadin and Ryze are a difficult pair. You can counter him as much as he can Counter you. His passive protects him mostly from ap Burst, which earlygame is the Thing you do not have. Your power lies in Extended fights with many combined procs of weaker spells which together form a burst sequence due to the short time. But kassa has his stupid mobility from his R and can one shot you if he gets ahead. Plus. Kassadin Q cancels your R cast, so be careful of your surroundings when you use it.
Is an easy self explanatory case. Whoever gets his combo first wins the trade. Careful of his roams, ward well and lock lane so he cannot leave it.
Same as Talon. But his roams are a lot more reliable and dangerous
Is the most difficult one probably. He can DESTROY your face if he gets his combos off, but as ryze you can effectively trade back. Use E-W-Q to proc your shield and Reposition yourself while he is rooted to deny him a lot of damage after he ults you. Apply as much wavepressure as you can when his ultimate is down, because he cannot trade you without risking death. But he can poke reliably and counterbuild you.
Champions you should not pick ryze into:

Why you should not fight any of e is mostly very self explanatory, so i won't write an explicit Reply on this unless you REALLY want me to, in which case i would Edit it in.