He's pretty easy to go against even if you are squishy when you play/build against him correctly. His ult is is a pain though, and it's one of the things I hate in this game. I hope if he ever gets a rework, they look at that. However it's just one of those things you have to endure, not unlike a Teemo lane.
The only glaring problem with a Tryndamere lane is he can get way out of hand if he gets a kill. Whoever loses the lane loses it badly. If I get the kill, then I'll probably get boots and start roaming. I usually play high mobility champs though that are great at split pushing. If neither of you get that kill, then it will be an incredibly boring and drawn out lane. That is the annoying part of Trynadamere IMO.
It's important to try to get that kill pre 6, so if you feel you can't do it yourself, ask your jungler for help. Don't be surprised to see the enemy jungler in your lane earlier either. They're going to want Tryndamere fed early. He has a weak early game, so use it to your advantage. He has to push the wave, so punish him as much as possible. Avoid trading with him when his fury bar is high.
These are great items against him.
You need ignite also for after his ult duration.