About
This guide will be focusing on the tactics I personally use to play Ryze based off of my experience since my very first tutorial with him.

I'm not going to tell you what runes to use or what items to purchase in what order, do so according to your weaknesses. learn to use runes and items to balance yourself out to your own needs. some people need more defense, some people have it down and want more offense, do what is smart for the win. the runes and items i have on this guide are just general types i clicked in order to give a feel. don't follow them exactly.

Basics

Ryze is a mage based attacker. If built properly he possesses the potential to harass early game, tower lure effectively mid game, and burst with supreme power end game. Ryze posseses very little health, high mana, and all instant cast abilities; This makes him a glass cannon.

abilities
Q - an instant attack boosted by Ryze's ability power and mana with a medium-large range
W - an instant, powerful stun that also does damage
E - an instant cast bouncing type ability with the potential for major damage if harnassed properly
R - an ultimate ability with no mana cost and a short cooldown, this ability is extremely effective when nuking mobs or rushing groups of more than 2 enemies

Content
1. Introduction - you are here!
1b. General information, skill sequence, summoner spells, pros/cons
1c. Abilities in depth. if you don't know them, you cant use them properly!
2. Early game strategy with takedown, farming, and lane tactic tips.
3. Mid game strategy
3b. Mid game tower lures and rushes - advanced breakdown
3c. Mid game XP/Gold boosting strategies - advanced breakdown
4. End game strategy
4b. Bursting in depth

1. the glass is half empty; the glass is half full
The pros and cons in any mage are evident from the title. Glass cannon. what does glass do? it breaks when you flick it. what do cannons do? blast enemies from afar.

2. so you think you know a good spell
There are two necessary components in a successful fight; Health, and Mana.
Instead of telling you that obviously heal(+summoners resolve from masteries) is absolutely 100% needed, and that not having an extra surge of mana(+summoners insight from masteries) for that last burst round is probably a bad idea, ill just dispell your current views on the other popular choices.

[smite] - no. just no.

[surge] - this skill is for melee attackers to get in, burst, and get out. not for you who should never be in the thick of things and need a burst of damage on top of your already powerful burst.

[flash] - again, as a spell caster you should never find yourself in the thick of things; your most evident responsibility is keeping track of the enemy team and NOT being ganked.

[teleport] - i have battled with teleport vs clarity for weeks and i have a simple resolve; teleport is a huge advantage early game for melee players to get back because they will likely take damage by having to get so close. However, before level 10 a caster should never be in melee range of any opponent, this is what your powerful stun is for. if you stay away in the beginning you will not have to go to base to recharge and need tele to get back so you dont lose xp. more on this in section 2 early game farming and harassing.

[exhaust] - if you rotate properly you should never need this due to Ryzes unique fast paced cooldowns and powerful stunning capabilities

[ghost] - again, a purely situational to ganking spell.

[revive] - Don't even begin to believe this is worth a spell slot.

3. To win or not to win - that is the sequence
e, w, q, e, w, r - after you get your R(ulti) switch back and forth on e and w as you see fit till your specific midgame (midgame and level have nothing to do with eachother, sorry!) after that you want one in q and one in r then max e and w and then go q, dont take your r above 2 until last its unnecessary as you only need it for minions!

Q
Q is your instant attack - it has a pretty good range and can be used to hit and run for harassing, ksing minions, and bursting

W is your paralyze - Ryze has a particularly strong paralyze because if you cast it FIRST, your next few abilities will re-leave its cool-down by 1 second each giving you the potential to have it ready incase they run

E is your bouncing attack - This attack is the MAKE OR BREAK in your burst and using it properly will decide if you die or live in most situations. this ability needs to bounce back and forth in order to do damage so placing it properly is a neccesity. This ability WILL bounce from minion to minion, from minion to champion, from champion to champion, and from you to champion, it will NOT bounce off of your allys so do not use them as a conductor you sick man!

R is your ultimate - This ultimate makes it particularly easy for Ryze to farm a huge group of minions, use it A LOT. any good Ryze will tell you the same thing. Refer to my technique on taking out a wave with it, taking out a wave, taking out a wave with it. it should always be ready by the odd wave! only use it on full waves, don't waste it.

1-6
From level one through level six you should have a strict harassment policy. If your enemy is 3 minion units away from your range or lower, hit them and run back asap. if you think they will expect it, just double back and dont take the chance. the key to early game is sending your opponents back to base as much as possible so as to put them at a gold and level disadvantage.
Heal and Clarity come in MAJOR handy at this point more than any other point in the game. eventually you will start dropping hp and mana as you irritate your enemies and send them back over and over, when you are level 3/4/5 use CLARITY AND HEAL when you are AT YOUR TOWER with TWO ENEMIES and ONE ALLY - use this abilities in range of your ally to boost you BOTH in order to continue pushing your enemies back to the base to continue taking a gold and experience advantage - try not to return to your base at all until at least level 6.

first trip items-
TEAR and beginner boots

6-10
levels six to ten should be your next major push. you now have your ultimate and you should be using it on MINIONS as MUCH AS POSSIBLE! time your abilities to all be ready when a fresh wave of minions arrives - this will maximize your experience and gold intake. don't be discouraged if you don't consistently kill them in your first rotation at this early level!

second trip items- survivability
at this point you want to spend your gold on more armor and mana - i will not be picky about these as it is dependent on your enemy team, enemy champions, and enemy strategy. get what is necessary in the NOW.

Lane tactics
Most players will send a mage mid off the bat - this is a bad idea!
in the middle you want someone who can attack from a range, but not someone so squishy as this is the most nuked lane!
try to pair yourself up with a ranger or a melee attacker - you will be able to persistently irritate even ranged attack enemies and keep them off the melee attacker whos main focus early game should be minions as diving is ******ed at this level.
COVER YOUR TEAMMATE IF THEY CANNOT ATTACK FROM AFAR! - enemy ranged attackers will irritate the melee first because its easier - its your job to prevent them from doing this to keep his health high until level 6! if they run in you must paralyze them immediatly and KEEP THEM OFF. do NOT dive, do NOT try to kill unnecessarily. your objective is retaining as much health and mana as possible - you will need it to survive until you get your ultimate. if you can do this before returning one time you will ALWAYS have an advantage!

11-14
this is where your bursting capabilities and farming capabilities REALLY start to shine! if there is mage or ranged attackers in either other lane help them nuke their enemies with your paralyze - other mages will benefit from Ryze's abilities even moreso.

at this point your aoe damage should be just enough to kill a whole wave of minions in one rotation. for the next wave you use regular abilities as each cast will reduce your ultimates cooldown, so by the 3rd wave you should be ready to aoe again. continue farming the unoccupied lanes in this fashion to gain a HUGE advantage in levels and gold. make sure you keep tabs on enemies! never travel too deep into a lane alone! (past 2nd turret)

lures
the most simple lures are hidden ally lures, and turret lures, these lures can also be combined.

turret lures
a simple and effective takedown method, bring your enemy within turret range and paralyze them, your turret will do most of the damage and even if you die and the turret kills you will usually get credit

hidden ally lures
the title says it all! when your ally from another lane disappears and goes mia and comes and hides near your lane its your time to shine. the kill relies on you!
right now its all about timing, get your enemy in the perfect position for a surprise ambush. at the beginning paralyze them, them unleash your Q, then your E, your ultimate is not neccesary as it is small aoe incriments, but if you decide to use it, pop it right as you click paralyze on them for perfect powerup timing. dont be afraid to play with your timing - it may take some time to get this down.

so lets say you are level 6 fresh, just got new items and healed up, just getting back to your outter tower with a full wave of enemies and friendlys. bust out your ultimate and use your Q on the mages, your E on the melee, and then autoattack on the mages, then the melee, this should take care of all of them within a few seconds.
next wave will be a full force of friendlys and a wave of enemies, take out the enemies.
next wave will be a medium force of friendlys and a wave of enemies, zerg them again!
next wave you should be at enemy tower range, take out enemy minions again.
next wave you should be right up in their towers face with a medium wave of friendlys and a fresh wave of enemies with a fresh wave of friendlys almost there - zerg the enemies and then focus on the towers so your friendlys dont get killed while you wait on a fresh wave - this will enable you to continuesly attack the tower without delay and take it out.
repeat this technique in different lanes for maximum farming.

15-18
13-17 is your window of maximum potential, if you master the correct balance of lane clearing with your aoe and zerging enemies from the shadows to boost your allys you should fly through these levels. at this point the game should be cake. continue pushing your waves of minions through as much as possible as THEY are MUCH more important than you when you get to the enemies base. when you have a LARGE amount of minions at the inner tower in one lane, zerg the tower and inhibitor with atleast 3 allys and begind spawning your first waves of super minions. continue pushing these large groups of minions into deep field and zerging inner enemy territory with them.

Your end game bursting capabilities are insane as a Ryze; heed one warning. NEVER. TRAVEL. ALONE. at this level you will still DIE easily, but you will be able to output TREMENDOUS amounts of damage in short bursts and clear waves of enemy minions in seconds flat. stay with someone, stay alive, keep pushing.

when you go in for a burst remember to always paralyze first, this gives you a few seconds to get into place for your attacks, and gives your attacks a chance to reduce the cooldown on your paralyze so you can use it again when they run if they survive that long.
master your ability to bounce your E, you NEED it to hit your enemy as many times as possible or it just wont work!