This is a short Summary how to build a Mid-Ryze.

The only summoner spells that are worth to pick, are FLASH and TELEPORT.
They grant you high mobility and the best escape skill.

Get EXHAUST only, if nobody of the team has it.

All other summoner spells are only reasonable if you have a team and you play a certain role.

For the masteries i take 0/3/27.

3 Points in magic resist because most mid champs are Ability Power Champs.

27 points in the 3rd tree give you maximum of Mana and manareg, maximum movementspeed, maximum exp gain, little spell vamp for early laning, longer buffs, 6% cdr, good HP regeneration and cdr of your summoner spells ( Teleport and flash ).

This gives overall very good early game(laning phase) because of the magic resist, mana reg and spell vamp, also longer blue buff at begin (around 7.40) if your jungler started at blue.

You have high mobility in mid game with short cooldown of teleport and +2% movement speed ( +4,5% with runes).

In lategame you have some more mana=more damage, HP reg thanks to the mana, and a EXP advantage.

Greater Mark of Insight ( 9x + 0.95 Magic Pen ) = more damage with spells
Greater Seal of Knowledge ( 9x + 21 Mana at lvl 18 ) = more mana= more damage and staying longer in lane
Greater Glyph of Warding ( 3x + 1,49 Magic Resist ) = Less dmg in early game for better laning phase
Greater Glyph of Celerity ( 4x + 0,9% Cooldown Reduction ) = Boosts your overall damage output(more on lategame)
Greater Glyph of Knowledge ( 3x + 25 Mana at lvl 18 ) = same as Greater Seal of Knowledge
Greater Quintessence of Swiftness ( 3x + 1,5% Movement Speed )= Higher mobility for ganks, being fast everywhere, dont loose exp or cs, dont miss dragon or baron fights, dont miss any teamfight!

Start with Mana Crystal for more Mana( = More Spells = More damage = More harrassment and gold of cs ) and 2 healing pots for surviving.
Then rush for the tear and start spamming spells. You have teleport and high movement speed for fill up your mana and get to your lane fast.
Get boots then and start building your Catalyst. If you have many ADs in opposite team get Glacial Shroud first. Then go for your Sorc boots and then finish the other item. Next go for the Banshees or Frozen Heart. I go for Banshees first because it blocks a spell and its so very usefull. Finish your Archangel Staff and the game should be pretty much over. If not get the Hextech Revolver and Upgrade it, or if u know you get focused, get Zhonya's Hourglass first.

Thats your complete build. You are one of the strongest lategame champs and nearly unkillable. If your positioning is good you can solo the enemy team.

The skill rotation is very easy on Ryze. If you play him some times you will know what spell is best in each situation.
Feel free to use your ultimate against creeps. Maybe just not if u see a teamfight coming or an other important situation.

Ryze is a mana-dependent lategame nuker.

Earlygame: 5/10

Midgame: 7/10

Lategame: 10/10

Have map awareness like with every other champ and talk with your mates what you will do next.
Succesfully communication is the key to win ( Even more if you have teleport and can help in situations where the enemy dont expect you to come )

Good luck and have fun with Ryyyyyzzzeeeeeee... bzzzz.