Not Updated For Current Season
This is basically just a build but I'll give some pointers.
Level up bloodlust as much as you can first to keep your health up. Spinning slash next because it does good damage in a fight and its your best method of escaping.
The thinking behind this build is that you get the infinity edge as soon as possible for the crit damage bonus. Then, you get two phantom dancers so that you will crit every time and fast. You should be hitting for around 700 damage by then and multiple hits per second. If there are any tanks you get the black cleaver, but if not, the black cleaver can be switched out for another bloodthirster. I find that Tryndamere's ultimate is all the defense he needs, so no defense items need be bought.
You may want to use some crit chance runes to help your early game, but I don't find it necessary.
You will want to master your early game skills. This is key to doing well as Tryndamere, as he doesn't do well until he's built. When laning, don't attack until you have a few bloodlust stacks or you won't be able to do enough damage. The summoner heal helps a lot if used the moment after undying rage expires and you are running away.
The finished build is:
The Black Cleaver