Hi, I go by Millionaiire on Mobafire but Highgate in game, I'm only silver so it's pretty obvious I'm trash at the game but I've spent a fair share of time playing Ryze, currently my highest played champion and I have over 90,000 mastery points on him. I spent a lot of time fidgeting with different builds and I found an unorthodox one that worked for me, hopefully it works for someone else as well. This is my first guide and Ryze is the first champion I've been confident enough in my abilities to create a build about, I am open to any and all comments and criticism is very much welcome.

REMINDER: All of this information is purely opinionated and based off of what worked for me, you may not agree with what I have to say and that's okay but I'm sharing what I believe to be the best build and playstyle for Ryze in my ELO.

Pros:
+Great waveclear
+Good kiting champ
+Strong CC with low cooldown
+Great vs melee tops
+Tanky late game with right build
+Big late game mana pool

Cons:
-Very mana hungry early game
-Weak vs long range champs
-Complex itemization
-Hard to play, harder to master
-No reliable escape, often camped

Flash is always a must in any scenario you play Ryze. Does not matter. ALWAYS. TAKE. FLASH.
I believe teleport is the best option for Ryze top due to the fact that early backing due to low mana is very common, also it is standard to take teleport in top lane and if your opponent takes it and you don't you can find yourself in some sticky situations.

Passive: Ryze's spells deal extra damage based on his Bonus Mana, and he gains a percentage increase to his maximum Mana based on his Ability Power.

Q: Passively, Ryze's other damaging spells reset Overload and begin to charge a Rune that can be used to empower Overload.

On cast, Ryze throws a charge of pure energy in a line, dealing damage to the first enemy struck. If a Rune is fully charged, Ryze also gains a shield and Movement Speed.
Passive: Rune Prison and Spell Flux reset Overload's cooldown and charge a Rune for 4 seconds, up to 2 Runes.
Active: Unleash a runic blast, dealing 60/85/110/135/160/185 (+45% Ability Power) (+0) magic damage to the first enemy struck. Any active Runes are discharged.If 2 Runes are discharged, they Overload, shielding Ryze from 0 (+60% Ability Power) (+0) damage and increasing his Movement Speed by 25/28/31/34/37/40% for 2 seconds.

W: Ryze traps a target enemy unit in a cage of runes, damaging them and preventing them from moving.
Instantly root an enemy for 0.75 second and deal 80/100/120/140/160/180 (+60% Ability Power) (+0) magic damage.

E: Ryze releases an orb of pure magical power that damages an enemy and debuffs them. Ryze's spells have additional effects against the debuffed enemy.
Apply Flux to an enemy, dealing 50/75/100/125/150/175 (+30% Ability Power) (+0) magic damage.
Spells consume Flux for bonus effects:Overload: Deals 40/50/60/70/80/90% more damage and spreads to nearby enemies with Flux.
Rune Prison: Root duration is increased to 2 seconds.
Spell Flux: Spreads Spell Flux to nearby enemies.Spells that kill enemies affected by Flux spread Spell Flux to nearby enemies.

R: Ryze creates a portal to a nearby location. After a few seconds, allies standing near the portal are teleported to the target location.
Ryze opens a portal to a location up to 1750/3000 range away. After 2 seconds, all allies near the portal are teleported to that location.If Ryze becomes unable to cast or move, Realm Warp is cancelled.

Wave clear combo: E minion>E same minion>Q wave
This combo spreads flux throughout the wave (and hopefully the enemy) then Qing any minion with flux provides extra damage to quickly clear the wave.

Full combo on enemy: E>W>Q>E>Q
This combo provides a full 2 second snare to the enemy while allowing you to output the most damage with the highest change to land the skillshot, also provides you with the shield and speed boost for landing E and W before Q.

Quick poke combo: W>E>Q
Must be performed quickly, if you W first the snare is much shorter but if you're fast enough you can land all 3 abilities while they're snared. If you aren't fast enough you can use E then wait a second to see where the enemy is running then predict the Q and hopefully land the skillshot for max damage, the more you play Ryze the faster you will ble able to perform this combo.

In depth item reasoning:

Start with refillable potion and sapphire crystal to partially build into corrupting potion and tear.
Buy corrupting potion and tear on first back, corrupting potion for better sustain in lane due to high mana usage and an early tear because it takes longer to stack on Ryze than any other champion that takes tear.
After corrupting potion and tear are built, start progressing towards Rod of Ages, I typically get RoA built around 13-14 minutes into the game which makes it fully stacked at 23-24 minutes, that's not a bad time to have a fully stacked RoA while also building towards Archangels.
Next after RoA is Archangels, gives lots of mana which in turn provides AP due to Ryze's passive, and when it's fully stacked and turns into Seraph's Embrace, the shield is huge to use in combat and to bait yourself.
The rest of the items are purely situational, you have your core built so all you need to do is examine the enemies to determine what to finish your build with, I almost always find myself buying Zhonya's Hourglass in every game.

The biggest issue people have with laning on Ryze top is running out of mana. Even after buying tear early mana can become an issue, it's not until late game you can truly spam abilities.

I personally like to go aggressive to start, using my E to last hit when needed and doing the quick E>Q combo to get off damage. I find myself backing early to get tear and corrupting potion and teleporting back, my second time in lane I last much much longer due to the sustain items purchased.

Warding is crucial when playing a champion with no reliable escape. Your level 1 R doesn't give you much to work with in terms of escaping so your best bet is to ward up and be aware of where the enemies are, one of the biggest mistakes I see in Ryze tops is lack of map awareness.

Ryze top is not a very strong early champion, your full combo obliterates your mana pool early and you tend to be very squishy compared to typical toplane champions. Don't do anything crazy early and if you make it to midgame in one piece, you're set.

When teamfighting begins in the match, if building correctly you are starting to see some of your tankiness show. Compared to your midlane and ADC you can take more burst and withstand combat for longer. I usually find myself towards the front of the pack in teamfights, due to the low range abilities and above average tankiness, it's the right place to be. If a squishy champ takes one step out of line in a teamfight, Ryze should be there to land his combo and burst them down while simultaneously rooting the champion for your teammates to follow up. Ryze is good at engaging behind the tank if you can spread spell flux the the full enemy team if they're too close together. Ryze is also exceptional at clearing waves late in the game and can use that as an advantage when pushing up on the enemies.

The few tricks the Rune Mage has up his sleeve are centered around his ultimate, the more commonly known trick is if you cast your ult then use Zhonya's on top of it, you're guaranteed to go to the destination of your ult. Very useful for escaping when caught in the late game.

The lesser known trick is if you cast your ult and you're standing on it, if you begin to recall you will not follow the ult. You can use this to bait enemies into running back towards you for the easy kill and also trapping enemies by seemingly being two places at once.

All in all, I've been playing League of Legends for a few years now and don't have much to show for it, however I do feel like my build for Ryze has worked well for me and it may work well for someone else. Ryze is my most played champion and I stuck with him through all the reworks and nerfs. Now he is in a very good spot, not banned too often and does a fair amount of damage. If played correctly he can be completely unfair and if the enemies are complaining that he needs to be nerfed again, you're playing him to perfection.