Ryze is a Mage-Assassin Champion that specializes in ranged Ability-Power based Area of Effect damage. With the correct item build, good farm and play style, he can be a powerful ally to your team. I am not currently ranked, but have played many games and have read just as many blogs.

I prefer to use a different Rune Setup then most for Ryze: Ability Power per Level Runes, Seals, and Glyphs with Health Quints. The reason for this is that I feel that with Items, Masteries, and Ryze's inherent ability to lower resist with Spell Flux, you will not need the Magic Penetration Marks that most Caster Carries need.

Pretty standard 9/0/21, maxing out Expanded Mind for the synergy with Overload.

Many people recommend that you start with a Doran's Ring for a better early game, but I would start off with Meki Pendant for more mana regen for harassing with Spell Flux as well as getting a good to start into Tear of the Goddess. Tear of the Goddess will later build into an Arch-Angel Staff which is imperative to Ryze. His Overload deals increased magic damage based on a percentage of your total mana, so this item synergies well and will give you higher damage output. After Arch-Angel Staff, I usually follow up with a Rod of Ages, Rabadon's Deathcap and then Lichbane to land some decent auto attacks in between spamming. From there, if the game is still going on, I suppose you could go for some defensive items.
Mejal's is always a good item if you're not getting focused or you're getting fed.

Start with Spell Flux Ability, moving onto Rune Prison and then Overload for the first 3 levels. From here you'll want to max out Spell Flux and Rune-Prison simultaneously. The reasoning behind this skill sequence is that 'E' is a great harass for early game as well as providing some great much needed Magic Penetration. As for maxing out your Rune-Prison before Overload, you are doing this because the DoT applied by Rune-Prison is some substantial damage, especially before you even get the mana pool to really take advantage of Overload's scaling with your mana pool. Your Skill Priority should look something like this: R -> E -> W -> Q

Flash and Ghost seem to be the most appropriate Summoner Spells for Ryze and I'll explain why: Although he may have Rune-Prison as an escape mechanism; being as squishy as Ryze is, you will have a much greater chance of escape/closing in for a kill by using these two Summoner Spells. They will both continue to be useful throughout the game when you are trying to position yourself for some clutch Spell Flux bounces.

Farming with Ryze is fairly difficult early game