Tryndamere usually builds exclusively attack speed and crit chance. Building items like Frozen Heart and Randuin's Omen cut his damage output significantly. If you can slow his attack speed, it becomes very difficult for him to deal with you; he's usually a pretty squishy champion because he relies on his heal and his ult to keep him alive. Also, if you can CC him before he uses his ult, you can kill him before he can get it off. If you can poke him down, you can also get him to burn his ult before a fight, which is very good for fighting him. Tryndamere is also more of a splitpusher than anything, so having strategies to deal with that are helpful. Champions like Jax would probably work really well against Tryndamere since he can dodge a lot of damage with Counterstrike, as well, Jax is also a splitpusher and probably one of the scariest 1v1 champions in the game. I would assume Nidalee, Gragas, and Lulu can do decent vs. him, especially early, since they can poke him down, kite, and CC (Gragas and Lulu) him around, as well Nidalee is a great split pusher, and Gragas has amazing (less now, but still good) waveclear in order to shut down a split push.