Play a lot of Tryndamere myself. Here's a few things that should help you deal with Tryndamere:
- Hard and even some soft CC: Things like stuns and roots really annoy him at the very least. If he can't move he can't hit you or spin at you. He can ult while under any form of CC but I'll get into that. Slows also help because it makes it a bit harder for him to get to you without using his spin.
Side Note: It's best to save hard CC if possible for when he uses his ult to waste as much of the immortality as possible.
- Ignite: This one is pretty simple. Ignite not only reduces his Q healing but can also guarantee a kill. It outlasts his ult if used at any point after its activation so as long as you can get him to 1 HP during his ult an Ignite can do the trick. Saving it for as close to the end of his ult works the best because he'll likely save his Q for then and you'll want to burn through that heal
- Armor: Pretty obvious. More armor on you means less physical damage from him. Rushing a Randuin's/Frozen Heart or even just a Warden's Mail severely hinders his dueling potential against you earlygame because it slows his attack speed as well. If you're playing a tank top, building both will shut him down if he tries to fight you.
- Range: A Tyndamere that isn't fed and/or doesn't have full build is easily kited by ranged champs. As well, he just can't lane well against ranged tops, especially Teemo and Quinn who both have blinds which help them even more against him.
As for some counter picks, Teemo is absolutely one of his biggest counters. I get mega salty whenever I have to play Tryndamere into Teemo. Other counters are pretty much any beefy champion with hard CC. Renekton, Ryze, Jax, and Malphite come to mind. Renekton is just a bigger lane bully than Tryndamere, Ryze has his crazy snare shenanigans, Jax's kit almost completely counters Tryndamere's, and Malphite gets extra armor and has an attackspeed slow to go with Warden's Mail. Other good choices include Nasus, Garen, and Darius. Keep in mind however that a particularly good Tryndamere can play around these champions, though Darius in particular is an especially good choice as his bleed along with Ignite will often kill careless Tryndamere through his ult.
General tips for laning against Tryndamere:
- Bully him off your minions if you can so he can't build up rage, and try to get your jungler to gank if he does manage to get some rage to try and force him to use it if you can't yourself.
- Try not to Flash away if he hasn't spun at you yet because he will follow you with it if he feels he can do more damage or kill you.
- Build a Warden's Mail early as I mentioned earlier even if you aren't playing a tank, it helps.
- Do not try to fight him level 1, you will regret it.
- This applies to most champs, but definitely keep your distance or even hug your tower if he manages get a couple kills on you early. Giving him more kills is the last thing you want to do.
- His Mocking Shout actually lowers your AD, up to 80 AD reduction at rank five. Many will max this second and some extra cheesy players may max it first. This gives him considerable trading power and should not be ignored if you're an AD focused champion like Riven.
Edit: Something important to note is Tryndamere will usually try to split push as much as possible since his teamfighting is so bad. Even a behind Tryndamere can turn things around for their team if they split push at the right time. Assuming you're beefy enough, just showing up to stop his pushes helps though it may not be entirely ideal at times as your team might need you for fights. Basically, you deal with him as you would other split pushers, so there's not much to write about that here.
It's rather late here, but this is everything I could think of off the top of my head. I'll edit in more if I think of anything.
I really think Tryndamere isn't a particularly hard champion to play against if you know how. He honestly isn't terribly strong in lane, though he is coming back with tanks falling out of favor and does best against squishy toppers. As well his team fighting is awful and feels like a less reliable Master Yi.
Sorry for the really long post, but I hope this helps!