-Always buy 2 wards everytime you go back.
-Play safe early game
-Coordinate with the jungler
-Get the second blue if possible to farm and harass more effectively
Ryze is possibly the best counter to Ahri. He has superior range harass with his Q and his stun can lock her down from ulting. He has very good sustain and if you get early MR she doesn't really do damage. Just avoid her charm like the plague.
On the other hand, Cass is the best counter to Ryze. Her constant harass and insane range and DPS are better than Ryze early game and possibly mid game as well. It's a good idea to ban her if you first pick Ryze.
Gragas has a pretty weak early game as well, but his range and huge nukes allow him to farm from a distance and steal jungle. He can be very hard to shut down and he will out damage you mid game.
Similiar to Gragas, he has long range and is hard to shut down. His massive Aoe and range can annihilate your team before you have time to react. Your best bet is to coordinate with the jungle to get constant pressure on him. Get a
early if you are getting combo'd. Your snare has no effect on him as well when he is in his artillery mode.
Ryze is a good counter to sion because you can QW him which blows his shield before he can stun you. Your spells will be up again before his shield is up, so you will be able to deny him farm and snowball the lane in your favor.
Ryze is a good counter to Kass if you get BV before FH. This will knock out most of his damage and you can just zone him mid game. Early game use auto attacks +
to harass and he will only be able to Q you. If he uses his spells on you he will most likely be missing a lot of farm. Make sure you farm better than him and once you get blue just start zoning.
TF is a pretty common pick. Generally people play him wrong and he's easy to beat, but it depends on the skill level of the player. If you are vs a good TF he will just farm from a distance and push lane all day and gank your other lanes. It is important to ward the side bushes to see if hes going to gank so that you can ping and counter gank. Mid/late game you can easily stomp him 1v1. If you get a snare off on him hes dead as long as he doesn't have MS quints.
Another champion that Ryze can match up well against. He loses in the early lvls to him, but once you get tear and blue buff he cannot trade with you, unless he gets an early advantage. As long as you stay even with him in CS and kills, you will win. Ryze's snare will stop vlad from moving while pooled which is excellent if the vlad doesn't know what he's doing and tries to pool out of the snare. Late game if you let Vlad farm he might out damage you because of his ult, but if you aggressive enough mid game you should be able to shut him down. He doesn't have a lot of CC but he can dive you if you are low due to his pool.
Pretty easy champ to beat. He is slow and it's pretty easy to dodge his Q with boots and MS quints. Kite him and move in between spells and you will easily kill him while taking minimum damage. Just make sure your team realizes he can ult and Ryze has no way to stop it. However, if he gets blue early and you do not, he will just out push you and will snowball with more CS than you. If you take control of both blue buffs he will lose horribly.
Almost impossible to beat early on in lane (if Kennen plays right), but Ryze is very good against Kennen in fights. He can snare him while Kennen uses his lightning rush so that he can not get in position to ult and sometimes you can make him waste his entire ult with a well timed snare. Farm as best you can and aim to outplay him in teamfights. Also, once you have your core items, you can easily 1v1 him.
Brand is a somewhat difficult matchup for Ryze if it is 1v1. He has very long range spells, a long stun, and can clear waves very fast. His weakness is that he is vulnerable to ganks if he misses his stun. Try to coordinate with your jungler to gank him. If not, play passive, farm and you will outscale him late game.
Morgana is a very strong laner due to the fact that she has a lot of CC, sustain, and AOE creep clear. However, Ryze can do well against her once he gets blue buff. She has no answer to his low cooldown bursts. Ward both sides of the river to watch for ganks, but you can play this lane pretty aggressive once you reach mid game and you have some items.
Very hard champion to beat if played to her full potential. She has so much harass and utility. With experience you will learn when her ball is out of position and can trade with her effectively. Her auto attacks HURT so do not trade autos with her. I would play this lane pretty safe unless you see yourself with an advantage. This lane varies according to the skill of the Orianna player.
If you need more help with matchups feel free to add me in game or leave a comment below.