When you face a Tryndamere you have 2 options, run or die. When you run, you have 99% chance you die. With his skills, no one is safe.

For runes i take full crit. damage. Combined with your passive, Bloodlust stacks and infinity edge you do massive damage.

If you want, you can change your marks into armor penetration.

For masteries i take 21-0-9 with improved Ghost and Exhaust. I take extra crit. damage and crit. chance. In utility i take lesser death time, because i hate being dead, and more exp for leveling faster.

I start with Brawler's Gloves and 2 Health Potion. This gives me 20% crit chance in early game. Wait until you have 700g and upgrade your Brawler's Gloves into Avarice's blade, for extra gold and more crit. chance, and buy your Boots. It is very important for Tryndamere to buy items with crit. chance whenever you can. This improves farming and killing.
After I upgrade my boots into Berserker's Greaves I start saving for my Phantom Dancer. Purchase the Cloak of Agility first, then zeal and then the Phantom Dancer.
When I have it I buy a Vampiric Scepter, that way I don't rely on my stacks to much and can I use them for damage. After that I want my Infinity Edge, this is the key item for Tryndamere because you hit tons of more damage. I start with the cloak then the B.F. sword and then the Infinity Edge itself.
Buy another phantom dancer afterwards, upgrade your Vampiric Scepter into Bloodthirster, sell your Avarice Blade and buy another one.

This build grants you 100% crit. chance and an almost unbeatable game. If you have full items, you have 50% lifesteal and a damage output of over 1000/hit. Every strike heals you for 500 health! In this point of the game, even Thornmail can't stop you.

Start with Spinning Slash as this is the perfect way to run and do little damage. Afterwards max your Bloodlust first, this is the way to heal Tryndamere in early game. I prefer maxing your Mocking Shout after Bloodlust because when upgraded, it slows more. I don't use Spinning Slash for damage, only for positioning.

For spells I take Ghost and Exhaust to be sure that the kill is mine.

So if you want to play Tryndamere and be sure of a game of ownage, use this build.

100% crit
massive damage
enormous lifesteal

I hope you learn from my build and have a lot of kills!

P.S.: This is my first build made, be sure to comment!