Farm! Freeze the lane at your end, and he will burn mana trying to farm with Q instead of farming with last hits. His mobility is for engaging, so you can get free hits if he last hits minions with melee, and he can't safely dive you with only E.
Also, if you push to his side, he can overlap his ulti on you to deal massive burst, but if the lane is near your turret, he has to save ulti for dives or to retreat from ganks, losing a lot of damage. Don't aim for the kill, he is a very safe champion, out farm him and force him to recall or build mana instead of damage.
Place wards in your jungle as he roams quite easily, if he does roam, and you know where the jungleer is, follow him. If he engages bot and needs to escape, stay near (no on) his shadow for free finishing blows. If he is running away, DON'T Chase, he jukes worse than wukong and Yasuo. I baited the enemy team around the entire map (I was back door bot, ran to drake, hoped over wall, went to inner mid turret, went top passed baron, then returned safely to my lane. My team tried to help and died like fools, but I had the enemy team chasing me for about 1/2 minutes while I was dealing damage with Ulti and poke. my ulti actually came off cd, that's how long they chased me for.
If you don't have MR or he's ahead, don't dual him. He will try to slyly place his stun over you, and he can ulti on the spot for massive burst. Poke and retreat, hit him while he farms, he has no sustain, so he has no way to get that HP back, unless he wants to waste ulti. Mana regen doesn't synergise with his kit well, bait his skill shots and dodge them, if he is low on mana he can only recall, as he can't even use ulti to escape anymore.
If you are ahead, let the wave push, then go aggro on him. force him to ulti early and he won't even be able to last hit a couple minions, he will be forced to recall entirely, Fiora is good at this. If he goes top, Fiora and Darius (if played really well) can punish him, panth as well, if he is mid, most assassins like LB will be able to bait and punish him for trying to farm, and stop him snowballing.
Haven't gone up against a yas yet, but Zed and Lb should beat him.
So yeah, biggest tip, like with Kata, watch out for his roaming, and cut off his farm, he will become useless. Late game and team fights he is very strong, so get ahead, DO NOT DIVE, if anything, roam yourself if your lane is pushed. Deny him farm, deny early kills, and get ahead with good map awareness and stop him from reaching Nasus-level late game, as his full build is oppressive, and hard cc followed by high burst is your only chance at taking him out.
And like singed, Do Not Chase