Well, as i mentioned, this is my first build so i don't know what to do. I'm just showing to you how i like to play Tryndamere. I start with Brawler's Gloves and some health pots, than i get berserker's boots to get tryn more fast. Getting Phantom Dancer will improve your critical chance and your attack speed too. At this point you will handle the fights lot better. When Infinity Edge is owned, Tryndamere will have a good AD and his critical's will do a lot more damage to the enemies. Now you should get a Life Stel item, i chose The Bloodthrister, which garantes me a great life steal with it's passive. Now i get The Black Cleaver, it is good to improve your AD and your AS, so you wont need to get another infinity edge or phantom dancer right now, it can handle both requests. And the last item i already get is Phantom Dancer, but sometimes i have to buy Last Whisper, because now he is giving ArP. It can help you a lot when you are fighting a team with some tanks or a good one.
So that's it. hope you enjoy it ;)