I've played a lot with Tryndamere and my stats after a game with him are 18-2 10-1 or sometimes even 15-0 ,so if you follow this guide carefully you will win most of the games with him.

Pros:
-A lot of damage
-Almost can't die
-Can catch almost anyone
Cons:
-Low hp and armor
-Weak at begining
-Maybe weak without ulti

All you need is little attack spead - 13.8% with masteries and a lot of crit/dmg - 36%.At high levels with Infinite Edge you deal 286% of your damage that can lead to 1028 clean damage which kills tanks with 5-7 hits.Beware of Thornmail tho,cus you kinda kill yourself!

Now the spinning slash is a tool for last hitting and for escaping.With it you can move through walls,so your pretty uncatchable.Then you must get B,because you take a lot of damage and people want to harras so you take bloodlust.At level 4 you must prepare for ganks so you need W(Slow).Remember that your W slows only when they're turned around,but if you fight against melle DPS you can activate it for damage reduction.You should cast your ulti when you are at low hp,but you decide.It depends on-Casters,nuke spells,DMG-over-time spells and so on.Remember you still take damage but you can't die,this isn't Kayle's ulti.

Tryndamere and Kayle are the only heroes with invincible ultimates.Tho a little different.Don't be mad if you didn't use your ultimate properly,it's better to use than death!

Vampiric Scepter goes great with our Q spell and a little later with emblem of valor makes you stay on a lane longer.Then we need Infinity Edge quickly for crit.Stark's favor is for attack speed and increasing the lifesteal.Phantom Dancer is obvious.You can get the Bloodthirster instead of Execuitoner's Calling if you don't die often.And Istead of Sword of Divine you can get if you want Youmuu's Ghostblade or Guardian Angel.

Ignite is for the lucky player or healing champions.But flash is good cus you have something like double teleport,good with running and catching with W spell.

Most likely Tryndamere will get banned in Ranked games.If he doesn't people there are a lot smarter and can counter him easily.See what your oppents get for items and try to find a counter.Wait for jumping in groups because you will be focused.Beware of Crowd Control