Not Updated For Current Season
Well, this is my first build for Tryndamere. It's not the best build, but it's a personal build I use for myself. I'd like to share it in hopes of seeing it on top of the list.
As Tryndamere, you're solely able to kill anyone and just about anything by yourself. Because of this, you might feel a little superior over the others, don't let that happen. (In other words, greedy.)
In early game, you want to start out with boots. I use this because 1 second can make a huge difference, that's what I believe. With your teammate, properly coordinate and time your gank. Be aware, the lower HP you are, the most chance of critcally hitting something. Use this to your advantage and get first blood.
In the middle of the game, you should have at least one phantom dancer. Kill Dragon yourself, and assist any allys that are in need of help. Also, check the jungle for any champion that happens to be in the area. You have an advantage due to your ultimate. Use it at the VERY last second you're about to die. Finish them and slash through walls for a quick escape from potentional ganks.
This is probably the most difficult part- ganking and maintaing your own HP at the same time. In order to distinguish your HP from others, you have to attack the person that is located the furthest away from team fights. Slash in the slaughter the enemy and escape unharmed.