The basics of this match up are, trade as much as you can while doing so unexpectedly, if he wastes W on a minion, it is a good time to go in.
You will want to rotate between freezing a wave (last hitting; attempting to prevent him from wave clearing), and then hard shoving the second the extra wave occurs.
This will keep you relatively safe in the meantime, and free from the constant poke and harassment, as you shove in the double-wave you gain a minion advantage early, so if you are ganked you may rely on the minions for a sizable amount of extra damage.
As you are against a Ryze, who relies on hitting skillshots (and doesn't have enough mana early to consistently full clear minion waves AND keep you off of him), you will be able to pressure him pretty easily, and this is important. Once your two waves are crashing together, you gain a distinct advantage in the forms of minion advantage (damage wise; fighting against each other you are almost guaranteed to win the trade), the ability for your minions to body-block skillshots (which Ryze relies on to do much damage to you), and simultaneously even if he were to engage on you, he would be losing out on the cs that is now under his tower. You gain an opportunity to trade for free on him while he has little recourse.
Gaining an advantage, and pressing it, is very important to success in top lane.
Here are links to Imgur for my build and stats
You take Conqueror for better sustained damage trading (especially against other tanks, where it matters most), Triumph for the healing and bonus gold (adds up over time), Legend Alacrity for increased attackspeed, and Coup for increased execute damage (definitely secured me kills I otherwise would not have gotten.
Conditioning and Bone Plating were used to better help with scaling, as I typically avoid heavy-defensive items, prefering to stack HP with offense oriented items.
Build wise, I took the magic resist early to better absorb damage, and recognized I needed greater burst, opting for Sheen. Completed Merc treads to better reduce cc, then finished Triforce, going for the defense stats of HP first while working on my Sterak's Gage, as I didn't need more directly-offense stats more than simple survivability that early into the game. Once completed, this item scales very well with your triforce, while also granting even greater defensive prowess than one might initially suspect. Swapping from this, building into my Titanic Hydra, grabbing a heavier focus on damage this time around as I've already completed two 'defense oriented' items (steraks and merc treads, both also useful in a myriad of situations), once completed it will give me a great increase in damage, without sacrificing defensive stats. Going for GA as my final item, I went for increased damage first, as it was the most expensive component I could afford at the time that would grant me the greatest chance of surviving (sometimes greater offense is better than minimal defense; i.e. one-time Zhonyas or cloth vs 40 extra AD), GA gives me a second life (which comes in handy at one point not shown on video).
Alternative runes would be Legend: Tenacity along with Unflinching in place of Bone Plating. While not granting as much attack speed, these combined with Merc treads will make you almost immune to non suppression and knock-up cc-types, great against certain team comps, useless against others.
Feel free to ask questions if you have any below, and I'll answer them as best I can.