People might call me noob but this is how i play ryze and this is my first guide ive done. I play Ryze as an AP Mid. he uses mana to boost his spells damage and. please try this out :).

Greater Mark of Insight: Gives you Magic pen to deal more damage with spells
Greater Seal of Resilience: Gives you armour so it helps you against AD champions
Greater Glyph of Potency: Gives you ability power for stronger Abilities
Greater Quintessence of Potency: Gives you more ability power then a glyph for better damage.

If you want a more of a way to start ryze of then you follow this:

Start of with either:
Boots of speed, and 2 health pots and 1 mana pot
OR
Mana Crystal (look on next chapter for complete guide of mana crystal

#note#
Starting with boots of speed gives you more mobility early game but you buy sorcerers shoes before tear of goddess then you buy rod of ages. then you basically buy the rest of the other items listed on the top.

Start with a mana crystal then build it to a tear of goddess.
Then buy boot of speed then upgrade then to sorcerers shoes ASAP
then upgrade the tear of goddess to arch angels staff.
then buy rod of ages, Deathcap, Void staff then the unholy grail.

The skills order above have all the skills but there are many combos to get your opponent low or killed:
E to deal damage + reduce magic resist, Q to deal damage, W to stun them there then Q again

Q,W,E,Q is another way to deal quick damage.

I hope you like my guide and use it to dominate as ryze! :)
If you have any ideas to help me with my guides can you list it on the comments so i can improve, Thanks.