Start at Red Buff (ask for some help here)
Wraiths
Wolfs
Blue Buff (pay attention)
(buy Madred's Razors....throw your Smite away!!)

when ganking DO NOT USE Mocking Shout as soon you engage, save it for when the enemy tries to flee or fight you, the slow is big but as you know, only work behind the target
keep that in mind ALWAYS
do not tower dive without Ult (you have no defense against towers)
tell the ADC not *****in when you get the kill, it is impossible to control your criticals
and they are high! really high!!!

Focus on 2 things

Madred's Razors/ Zeal/ Vampiric Scepter ASAP

and then

critical chance - Tryndamere have some, so, you need to balance between damage and crit chance, that's THE most important thing here

other suggestions (if you find some difficulty)

Statikk Shiv
Executioner's Calling
Sword of the Divine

focus on the REAL TRINITY (for Tryndamere)
Phantom Dancer
Infinity Edge
Bloodthirster
once you have this ...easier than may look...you will be 1k crits

NOPE!!!
you defense is...
attack, keep attacking, and when you critical strike someone you will see.

my record? 1200 per attack (they surrender before i finish)

Pros -
Absurd Damage
Good Gap Closer/Scape Tool
Thick Damage
easy sustain
Damage is like Law & Order - SVU
easy solo Baron when he appear (if you have the "Trinity")

Cons -
lvl 1~6 kinda hardy jungle (you need some help)
you are no tank, so, dont!
countered by burst damage/disabler champions
no disable, and slow is tricky to use!

Never tried!

Someone else needs to be the tank...and be ok if you get some kills
if they have some disable + your W....OH BOY!

see it for yourself?