Well, there are a couple of general tips I can share. As a note because your post doesn't say some of what you do and do not know about Ryze some of these might be to general. I'd be happy to share more specific tips if these are not really helpful.
After the mini rework Ryze needs to be build differently to reach the same kind of damage he had before the changes. Starting the game with a Doran's Ring is a lot better than it was before, but do note it can delay building your Tear, so knowing what match ups you can build a greedy Sapphire Crystal is very helpful. Building Tear of the Goddess into Rod of Ages into Archangel's Staff is still optimal. After that raw damage is often better than going into other mana items. Almost all the Needlessly Large Rod items have some place on Ryze depending on the game.
Also for masteries before the changes it was very common to play Ryze 9/0/21 to take advantage of the extra utility because his damage was so large late game you did not need offensive masteries. Post changes 21/0/9 is now more optimal, taking all the standard mage masteries as well as the flat mana and movement speed in the utility tree. For runes using percent movement speed is still very viable, and my personal preference, but if you are mid using flat or scaling mana can be very effective.
You have more flexibility in how you level your skill now. For early single target damage, and in most cases in fact, maxing Q first is best. If you are against a melee opponent that you can bully maxing W first for kill pressure due to the increased root duration can be really strong. Not optimal, but maxing E first for early wave clear against an opponent with great wave clear pushing you in constantly can be a good call, but often even in these cases maxing one of the other skills first is better.
For play pattern when you see your lane opponent sitting in their creeps that is when you want to harass them with E for bonus damage. Never be afraid to use that Ult. The cool down is insanely short. Just use it to quickly farm that wave, it will be up again before you know it. If you go to gank another lane be sure to toss a few Qs out to charge your passive before you get there. Having that shield at the start of a fight can really go a long way.
If there was something I did not do a good job explaining, or just something else you wanted answered, just let me know.
rework and he was my first champion ever purchased. I loved playing the Rogue Mage and he helped me learn a lot during my first few weeks playing. However, since his rework I've had great difficulty in grasping how too properly play him with the way he is now, especially with the recent nerfs to him in the latest patch. With that being said, I've made this discussion to ask for advice on playing 