Hi this is my first build and I'm going to keep working on it.
This is mostly for 3v3 which I play the most of and tryndamere shines.
I havn't figure out how to put link picture to items so if anyone wants to post how to too please post in comments. You might notice I'm no english major.

I allways start with Doran's Blade. the +100 heath really madders in early fights. I've had many early battles where I win with only double number health. After the blade I get Boots of speed. the boots plus mocking shout are the best early way to get a kill after your Exhaust is in cooldown.

Get boots upgrades to what your foes are building if they have slow or stun and have 2 ap heroes get Mercury's Treads, sometimes just two abilty power foe champions is enough to get them.
If they have 2 dps get Ninja Tabi. If there team is a good mix or your geting feeded Berserker's Greaves will help you keep ahead in kills.

Zeal is so you can keep getting those kills after that you really need damage to keep the kills up. never get Elixir of agility before zeal. Some times if your geting feeded you can get B. F. Sword before Pickaxe, which ever one you get make sure to get Cloak of Agility so you can keep those critical hits up. at level 7 after zeal anytime you can get Elixir of Agility Get Vampiric Scepter before Pickaxe if your behind on income, or want to kill dragon. at level 7 with Zeal Berserker's Greaves and Vampiric Scepter you can solo dragon.

Mid game I normmaly have Berserker's Greaves Zeal and Infinity edge.
At this point its normally the best time to get some armor to off set tanks massive armor
they dont have a lot of attack so a few armor puts them back a lot.

If your ahead you might wanna get [*] Phantom Dancer before any armor.
other options if they have a good dps carry like xin or tryn get Thornmail
sell Doran's Blade late game, if you need space.

Normally I do not get Elixir of Agility unless I have Exhaust to go with it, or I'm half way done with building [*] Infinity Edge and low on funds to get next part.

All critical runes, early game it gives you the ability to push at level 2 to kill other champs.

Ghost use it to run away before your ulti is over during a fight so you dont feed. sometimes the extra push of ghost will give you enough speed to get a kill before they get away.

Exhaust the slowing down champs is what gets your the most kills. at level 2 i normaly try to kill with 1 in spin and 1 in bloodlust. First get a few bloodlust once you have a few then spin to your foe use exhaust and start wacking away normally this gets your a kill unless they have flash and to close to turret.
Dont use Exhaust on yi once level 6, unless ulti is used up. use Exhaust on garen after he does his wirl wind attack.

if you plan of ganking early get spining slash first. otherwise get bloodlust.

Mocking shot:
I normally only use mocking shot if they are running away. Late game you do so much damage that if you mocking shot while in battle with a dps is going to get you killed.
after a get 2nd mocking shot I get a 2nd spining slash. to many times the cooldown on spining slash as got me killed or missed me a kill for not being faster.

Spining slash is great at moving your faster running or attacking.
Spining Slash gets you threw walls and is a safe-line during battles the best places to spin are left and right walls just above the lizard, and just below the dragon. Make sure hug the wall when you spin every time or you will miss going threw. At start of game if you are going to gank, Tryndamere can get to the bottom the fastest by using spining slash to go threw your bases wall. If you havn't tried it yet I suggest doing a custom game to see where you can spin threw and how close you have to be to spin threw it.

Endless rage: when to attack and when to run.
If foes have slows and stuns when you endless just go all out and kill everything.
If they have no slows and stuns or you have ghost then run away while endless is half over. Its allways better to run away alive then get 1 more kill and die.
Allways make sure to eat your bloodlust just before endless rage is over, if you didn't know useing bloodlusts heals you. a tactic to do if they dont have slows is before you die hit endless rage attack for 3 secs then run, with 2 secs left use spining slash to get away faster then with 1 sec left eat your bloodlusts. If one has teamates with him in a middle of a fight you can duke it out and keep fighting normally this is best of foes in some way another have a way to get to you so you can't run by it slows or they just to fast.

You have endless and full bloodlust at enemy turret has 1 guy with 3/4 heatlh kill the guy useing mocking shot as he trys to run then run away using endless so you dont die. If he runs to base wait till your out of turret range mocking shot spining slash to him and hack away. Dont kill enemy champions at turret before level 6 unless the guy is really low hp and you have wave back up, make sure his allies are away too.

Tryndamere can kill tanks if they are low on life. you do more damage then other carrys. So make sure you kill the enemy carries first. Have armor enough where you can ignore pure armor build tanks. Wait for your allies to lower the tank low enough where you can just hack him to death. This is best used vs thornmail tanks. If the tank is morde get force of nature so he doesn't hurt you much, low on cash just get Negatron Cloak.

patheon can be a problem early game unless your full bloodlust and have exhaust because he blocks attacks. champions like kennen dont waste Exhaust on because they still be able to run to safety early game. Anivia egg move will prevent you from killing her at turret even with rage. Its allso a good idea to have zeal before you think about killing Anivia.

Teemo's poison kills bad Tryndameres if you use endless vs teemo run away right away the posion effects only last 4 secs and endless rage lasts 6. Do not run from teemo if he has [*] Frozen Mallet. Vs teemo and shaco you want to pop dolls and shrooms when possible then heath with bloodlust.
Some times you can kill Fiddlesticks while he absorbing you if your gears right like resistance boots decent items, and crictal hits keep hiting. Most the time you just want to spining slash away from fiddlesticks when he uses his heathdrain spell.
Vs Dr.Mundo you can get Executioner's Calling and zeal, make sure to get some ad like pickage while your making calling. i would go zeal pickaxe Executioner's calling then get infinity edge starting with the big fvcking sword. Mundo is fast so you might wanna upgrade to phantom dancers before you finish infinite edge.

I've played some games with some defense masteries like dodge +4 and it really helps vs other dps.