Hello my name is Vlad.
I am player in league of legends on devision silver II.
i saw so much games with Ryze and I played with Ryze so much that I have the same build and i win with him most of the games with the same build.
i suggest to you summoner use with my build and change him a lot and tell me about better things to change.

Seal of Scaling Armor armor always good for ryze, resist of AD champions
Mark of Magic Penetration ignores enemy's magic resist
Glyph of Magic Resist magic resis good for ryze resist of AP champions
Quintessence of Spell Vamp spell vamp the bset way to restore your's hp back

Sorcery cooldown reduction for ryze is good for his abilities less time to wait to reset the skill.
Mental Force at level 18 you get +18 AP it is not the best but it is usefull in the start of the game.
Arcane Mastery this mastery give u 6 AP at the start and it is nice damge with the abilities in the start and you get plus famage of your's maximum mana.
Feast with perfect last hiting you can stay longer on the lane.
Dangerous Game for each kill 5% mana and hp restored back to op if you have much health and mana.
Archmage increases your's AP and it is awsome with rabadon but ryze is mana champion and alot of AP.
Arcane Blade 5% of your's AP to your'S basic attack is good because ryze use often with his basic attack.
Devastating Strikes magic pentertion good when you have mcuh mana and AP it is mean ignore alot of resistence of attacked enemies.
Havoc it is good with the Arcane Blade that give you 5% of AP to basic damage because it increases the damage with 3% more.
Meditation mana regen for ryze when he useing his abilities all the time he can the best thing .
Fleet of Foot usefull when you chasing some one or when you tring to escape for someone.
Strength of Spirit for each 300 maximum mana +1 health regen, ryze have nice Amount of mana and it is make better health regen .
Summoner's Insight less time to spells reset.
Vampirism more spell vamp more restored health back.

strat :
Sapphire Crystal good for the start gives you more damage in the skills and more times to useing abilities.
Health Potion useing to stay more on the lane and restor back your health.
Stealth Ward usefull against ganks or reveal bushes.

after the first recall :
Tear of the Goddess good items to ryze every abilitiy he gain 4 maximum mana for each abilitiy useing and give you mana regen.
catalyst the protector every level uping u restore 150 health and 200 mana over 8 seconds , this item is good for starting because u can stay more on the lane.
Boots boots good for cahseing and escapeing from someone.

late game items :
Rod of Ages best item for ryze because this item give to your's champion maximum mana and health every 1 min.
Sorcerer's Shoes gives you ignoring enemy's magic resist, also works with the mana damage not only with AP damage.
Frozen Heart gives you more mana and cooldown reducation, also good against ADC this items gives you armor and the attackers that attack you loseing their attack speed for few seconds.

all other itmes :
Will of the Ancients gives you more AP more cooldown reducation AND GIVES YOU Spell Vamp, by useing abilities on target restoring to you health back.
Spirit Visage gives you magic resist and cooldown reducation health regen good to ryze after team fight and incrases your's spell vamp by 20%
Seraph's Embrace this item is the upgrade form Archangel's Staff that gives you 1000 mana and mana regen and AP , active this item take 20% of your mana and gives you mana shield.