Amazing build both early and late game, will provide adequate mana regen early game and will allow for amazing sustinence of mana late game.

Tips:
If ur lacking mana early game, get someone to help u grab a golem buff (only if u cant nuke him down yourself of course). The cooldown reduction is amazing with ryze as his passive reduces cooldowns anyhow and the mana regen will allow u to keep stringing ur spells together to grab as many last hits as possible while still laning without draining down ur mana. Golem will also allow u to pop your ulti a lot more often and farm amazingly quickly.

Escaping with ryze is very easy, simply snare and run...

Combos:
Early game - R Q W E Q
Late Game - R Q W Q E Q

Why these summoner spells?
Flash can be used both to escape and to get close enough to grab a killing hit or initiate a 2v2 fight.
Teleport allows u to get in and out of lane quickly enough to grab ur items when u most need them and late game to help with teamfights or nuke down creeps to defend a tower which might be close to dropping.
Teleport can be swapped out with Ghost to chase players if they manage to escape with a smidgen of health, jus remember to respec to ghost in ur utility tree.

Why these items?
Sorcerers Shoes are standard for any caster champion.
Frozen heart will provide an essential amount of armor when fighting melee champions (this build rocks Pantheon's and Xin Zhao's) The mana it gives is also one of the cheapest mana boosts. CD reduction will also help a lot early game.
Archangel's Staff is just an amazing item to give moar mana.
Rod of ages will provide a mana boost and give you that extra health to survive for longer late game.
Banshee's Veil helps out when u start being focus during the initiation of team fights. It'll usually block a stun which would usually get u owned especially if youre being focused.
Manamune helps to cap your mana off and is obtained last to ensure you do that as quickly as possible. Can be obtained before a banshees or even before rod of ages just to help you get the extra damage around lvl 16 (which is when this build is most tested).

Conclusion:
Hope this build is appreciated... Ryze is one of the best 1v1 champions in the game at the moment and is fairly easy to play at the same time. i dont recommend him if u can use your hotkeys, but for all those smurfers out there, Ryze will be amazing for IP Farming and can literally win a game jus cause of his Nuking capabilities. Enjoy :D