The item purchases, are just any items that you should consider.
I used to play Tryndamere alot, but everyone complains that he is overpowered.

Here I will explain the main item order.

The Doran's blade, is a simple choice with 5% lifesteal, at the start this gives you a little bit more sustain.

Tryndamere is a good chaser but this early he needs this movement speed.

Brawler's gloves gives you a little bit of crit to hopefully, get you those lucky crits, you can need at points.

Avarice Blade, is more Crit chance, with some extra gold income which is always nice :D.

Finishing your boots is very important, and the extra attack speed is nice.

The Lifesteal is for more sustain, as you should be thinking about damage, not heals, you will get health back at the same time.

It's time for more damage, making your crits do more and Tryndamere own more, 2 long sword, then upgrading for the arm pen and cooldown is great.

The black cleaver, is more attack damage and speed.

Finally upgrading to one of the best end game items, with a ton of important stats.(The reason for upgrading it so late is because the extra gold from Avarice blade will really help)

The rest is more damage, but let's be honest if you've got this far you dont need it.

1) Last hitting with Tryndamere is a little different if your rage if full then you are going to get 100% crit.

2)Your slow only works when they have their back's turned.

3)Use you heal when you dont need the extra rage.

4)Your spinning slash is a great escape and chasing ability.

5)Your ultimate, is only worth using for staying alive, or holding in to help your team, I reccomend Cleanse, it is a popular move to ignite a Tryndamere as he ulties, double counter them, like a boss.

6)Your spinning slash does damage!, try to land this as many just miss, and just dont kill the target if you laned this they might have died.

7)With enough lifesteal and attack speed, you should be able to take on most things.

8)Stuns slows and silence's are your problem, in small fights target the one with most CC!

9)You might be fed, but your never unbeatable.