I get brawler gloves first because tryndamere is based on critical damage so I start with that first. I start building up for a phantom dancer because it gives 30% crit,55% atk speed, and 12% movement speed. I get berserker grieves unless you want boots of mobility to get back in the lane as fast as I can so I can level fast. Bloodthirster is next because it gives 60 dmg and some lifesteal so you dont have to recall any time soon.I choose infinity edge next because a tryndamere always needs the best critical hit as possible to win the game and get fed very easy.
I get trinity force at the end because it gives atk speed , 1.5x your next atk when used a skill , and a chance to slow the enemy champion.

(You may sell the boots when you get your 2nd phantom dancer because you are already fast by then) Ill recommend either a hextech gunblade for more lifesteal.