Hello and welcome to my first build ! This build will show you how i exactly play as tryndamere. I will appreciate if you leave a comment if u see something bad. So hope you like it :)

Pros One of the best "R" in the game :P , His W is very good slow , Awesome damage late game , Great ganker , High heal amount with bloodlust
Cons Squishy early game , Low damage with exhaust , Hard to heal with Ignite on , Focused on teamfights

Greater mark of desolation - Really nice counter vs. tanks + thornmails :P
Greater seal of resilence - I know u could think " You don't jungle why u take armor OMG ! " , but i like to harass other melee champions and this rune is really helps for doing that
Greater glyph of warding - You can take Greater glyph of focus too , but i find myself good in greater glyph of warding so i dont want to change it . Its only my opinion so feel free to try Greater glyph of focus too
Greater quint of desolation - same why i take Greater mark of desolation

Berserker's Greaves - Attack speed bonus + movement speed is really good for him.
Bloodthirster - Damage + Lifesteal ! The best thing Trynda needs.
Phantom Dancer - I like this item for attack speed bonus , movement speed if used W easier to chase + critical strike that any attack damage needs.
Infinity Edge - The reason i take it is because - YOU CRIT MORE !
The Black Cleaver - Attack damage that really helps Trynda in a battle , and AGAIN ! Attack speed that makes you attack faster + his anti-tank passive :P
Yomuu's Ghostblade - Attack damage + crit chance + CD reduction + its active is all what trynda needs

Best choice
Ghost - Excellent way to chase down your enemy
Flash - A great summoner spell for tryndamere, but i think Spinning Slash is enought for him.
Exhaust - Another excellent summoner spell. If your W is not enough to chase down your enemy just take it.
Just good summoner spells
Ignite- If there is a healer on enemy team it is very nice summoner spell just use it on them in teamfights or 1v1 and they will be useless
Cleanse - I saw some tryndameres in team using this. It is really good when you use your ulti and if hardly CC'ed just use cleanse and go away.
No way ! summoner spells
Revive - Your not planning to die anyway + you have your ulti
Rally - Just no ...
Clairvoyance - I leave it for supports
Clarity - You dont even use mana...
Smite - If you will jungle - sure take it.
Heal - You have your bloodlust.
Fortify - I will leave it for tanks.
Teleport - I dont know why , but i dont like it on trynda.