Use Overload's passive to optimize for maximum damage or maximum survivability.
Spell Flux's short cooldown allows it to be used to spread Flux to many enemies.
Ryze can move and cast other spells while Realm Warp is charging without cancelling the portal.
Playing Against Ryze
Ryze is especially dangerous to opponents that are marked with Flux.
Use Realm Warp's windup time to figure out how to deal with what may be coming out of the portal.
Crowd controlling Ryze during Realm Warp's windup will cancel the portal.
Even though Rune Prison is commonly maxed last due to it's root duration not scaling with ranks, it's a decent choice for a level 1 pick, since Overload and Spell Flux do little by themselves and early game mana doesn't allow for very many combos; addittionally Overload can be blocked by enemy minions, making it hard to land on champions during laning. Rune Prison can be used to halt the enemy if they attempt to burst you early.
You can cast an extra Overload between the Spell Flux and the Rune Prison for extra damage, but be aware that doing this will not trigger the shield as Runes will be consumed every time Overload is cast. Since Rune Prison has a long cooldown and you will be left with just Spell Flux to charge Runes, make sure to make the right decision between gaining the shield or the extra damage.
Overload can be used with relative freedom once enough bonus mana has been built, since it's cooldown is refreshed by your other spells should a fight break out. With just a couple of items and a few ranks, it does a decent chunk of damage even without combos to enemies who don't dodge it in time.
This full combo only works with near max CDR due to your E being cast twice. This is the main combo that you'll be using most of the time.
Ryze is one of the best users of Phase Rush due to his natural 3-part combo, which also stacks with the extra movement speed gained from Overload's shield; allowing him to easily both catch up or run away as the situation requires.
Electrocute is also triggered the same way, useful if you desire more burst damage.
The Domination tree also has Cheap Shot, which works together with Rune Prison for even more extra damage, and Ravenous Hunter is also a good pick as Ryze has no healing sources, and all of his abilities are single-targeted, giving him full benefit.
Ryze's abilities scale with both Mana and Ability Power, which makes items that have both stats much more effective for increasing his damage output.
Arcane Mastery gives Ryze bonus Mana based on his Ability Power. This makes Tear of the Goddess an essential item early game, since spamming abilities gives you bonus mana, due to its passive effect. It should eventually be built into Archangel's Staff, preferably when the item is fully charged, to get Seraph's Embrace as soon as possible.
Rod of Ages is commonly the first finished item as it gives Ryze everything he needs; ability power, health and healing, and mana as well as mana efficiency, all of which synergize with his abilities and make him more durable. The stats growing over time also fill up the gap between purchasing it and saving up for Archangel's Staff. which will usually be fully charged to transform into Seraph's Embrace by the time enough gold has been acquired.
Morellonomicon is a good 3rd item, as reducing cooldown for Spell Flux increases the frequency for Overloads, which will be extremely lethal from the extra AP and Mana it also provides.
Zhonya's Hourglass is a good situational item on Ryze, as the Statis can be used to guarantee a successful Realm Warp into safety. If Realm Warp isn't ready or should be saved, it can still give a couple precious seconds for Rune Prison to come off cooldown, allowing Ryze to escape or maybe even win the fight.
Abyssal Mask is surprisingly effective even though Ryze is a mage, as the aura has a longer range than Spell Flux's and Rune Prison's cast ranges, and together with Overload 4 it can give Ryze very good survivability even against burst mages. It does little to contribute to damage by itself, however, so be careful if building it early.
Ryze has a relatively short range for a mage so long range champions like Varus or Lux can harass him with less risk.