My Ryze build for friends who want to learn or play him, pretty easy now much to read as i tend to focus more on builds and stuff like that as the most fiends i have that plays LoL have good experience

You might be wondering why Hp per level on ryze?, well it gives you great sustain and overall more tanky than you will already become, i choose HP per levle over mana or armor because you dont really need it..
Mana regen is useless considering your jungler will most likely give you blue, if not then you will probably take it for yourself
armour, You're in mid against an AP carry, that does magic damage, so armor worthless

AP quints??, AP quints you might be thinking "But doesnt ryze's skills base off Mana?" Technically yes, however his E does not that much, early AP with theese quints give you higher damage not only on your E but Q and W aswell,

The build displayed above is pretty good, and its the one i run the most if not the only, of course there are different ways of using this build, like you can switch out frozen heart for earlier banshee or even rod of ages, however theese exact items are great, so you should really just adapt to which order althought the one displayed above is pretty good

Summoner Spells is pretty optional, and you should choose what fits you best however here are some good advices and probably the best choices..

Flash-Ignite. A great combination of spells as they give you both Damage, escape, and initiation,
Flash-Exhaust. You should really only take this if you're going against some really heavy AP, so you can shut down their damage.
Flash-Teleport. Rarely used, however a great combination especially if you have a great jungler with kill popentional, if you dont need either ignite or exhause pick up teleport, as it makes you be able to stay in lane if you die or forced back, but also that you can tele-gank, which basically means if you teleport to a ward or even a teemo mushroom without being detected as they are most likely in brushes, you can gank easily and most likely kill

In a teamfight as Ryze you should Focus down their AD carry ;Aka the biggest treat; now the AD carry of course is not always the biggest treat but most often is, especially in high level play, Simply take down the highest treat, primarially AP carry or AD carry, REMEMBER to use your ultimate in team fights as not only gives you stats, but all your abilities become AOE, which gives high damage espcially if they are chuncked up

Farming as Ryze is as any other character, you last hit the creeps with auto attack, however as Ryze you need not to miss a single last hit( impossible but you get my point), so dont be afraid to use your abilities to farm creeps is you cant take them all with auto attack as farming pays off really fast, if the jungler gives you blue or you take it youself, Try activating your ultimate and demolish a minion wave to push them to tower, now that the minions are push you not only got all the minions, atleast the most if you did it correctly, You can go gank a line, if no lane is gankable, go farm some jungle creeps, most commonly Wraiths