Ryze is a very combo-based champion. I haven't played the new Ryze much, but I have played the old Ryze and seen videos on his combos - not to mention I'm pretty good at stringing combos together just by knowing was the abilities do. Q resets whenever you cast another ability - this is important.
Your combos to practice are:
- Q+E+Q+W+Q+E+Q (maximum damage - Q is dealing double damage on all the casts just after E's)
- Q+E+W+Q (survive and kite, this is when you expect long fights to happen that you need to kite around or when you need to survive an opponent's burst and escape - 2 second root + the shield and ms buff on Q)
- E+E+Q (waveclear or if the enemy team groups up - 2 E's on one target will spread Flux to surrounding enemies, empowering the Q to spread and deal double damage to all of them)
- Q+E+Q (quick, short trade burst; this is your lane trade combo before you pick up your W or when you can't/don't want to cast W)
How Ryze Combos work: your Q will reset whenever you cast a spell, and casting 2 spells without casting a Q in the middle will give you a shield and some movement speed the next time you cast Q. In addition, your E doubles the effects of your other basic spells - Q deals double damage and spreads around enemies with the debuff, W lasts twice as long.
Go into a custom or something and just practice these combos over and over and over again until you have the muscle memory. As an old time Ryze player (he was the first champ I bought back in S1), I pretty much have Q E Q W Q E Q stuck in my memory. These other combos are new Ryze combos, but I still know them just from knowing his abilities' interactions with each other. Ryze is a very rewarding champion to learn, but he's difficult, too. Don't be afraid to test your limits so you know what you're doing 100%. His win rate spikes up to like 58% or something like that with over 100 games into him, so practicing and learning him is definitely worth your time if you're looking for someone to main and climb with. Lower average win rate generally means higher win rate with 100+ games, which means a high skill camp, and these champions will always be better for long-term climbing than champions with lower skill caps, but higher average win rates because you'll be able to outplay your opponents so much better as a Ryze main than you will as an Annie main, for example.
Last thing is items, runes, and masteries. I'm not sure what's best for Ryze in terms of runes, but masteries I normally would go Thunderlord's, not Stormraider's, and the best build is pretty similar to what it's always been: Tear => RoA => some AP stuff (Abyssal Scepter, Void Staff, Rabadon's, pretty much just AP/CDR until your Tear is closer to stacked) => Archangel's (probably 4-5 items by this point). Seraph's Embrace active, RoA, and Abyssal is a lot of defense: if you're against someone with a lot of short range magic damage burst (Fizz, Akali, Katarina, etc.), get Abyssal right after you have your RoA and Tear stacking and it should be very difficult for them to kill you. Pretty much, you're building to survive their burst combo and then afterwards kite around them with your snare until they die.
(Aahh, I remember the good old days, where you build Archangel's + RoA and then full tank on Ryze. Why? Because a lot of tank items had mana so your mana scaling made you able to build full tank and still do tons of damage)
game against 
and Ryze usually builds health early with RoA, but it didn't seem to really matter at all. Fizz' full combo was able to 100-0 over 1500 points of damage at level 7 with nothing but a 
and 
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