It is key to get your Spinning Slash and Bloodlust at the start so that you can get minion kills, and when low health, not have to keep going back to base. It is very important to get some kills at the begging so that you can get your Infinity Edge as fast as possible. Tryndamere's passive increases his crit chance as his fury goes up, he gains 5 fury for 1 attack and 10 furry for a killing blow (on a minion or player). When going into a battle with another champion having 70-100 fury will give advantage. Also Bloodlust consumes fury when you use it. The more fury it consumes the more health you get.

The reasons this build uses the items is has is because they work very well togerther.
Berserker's Greaves provide attack speed so you can gain fury faster (which goes from each attack), Infinity Edge gives you damage, crit chance, and makes your crits do 250% damage making it easier to fight of enemy champions, Stark's Fervor is a very important item because it increases you attack speed even more and give you life steal and health regen. When you have the first 3 items you are pretty strong because you hit faster, harder, and you gain health. After these 3 items are obtained, you will only have to go back to base to buy more items. When you are low on health, go into the jungle and kill some mobs to gain your health back. The second Infinity Edge provides even more damage and crit. If you haven't figured out already, Tryndamere get a lot of damage from critting. Because he gains crit from fury, with 100 fury he has 35% crit chance (0.35% per 1 fury) and 2 Infinity Edge's he has a total of 65% crit chance, this means he crits most of the time. Getting the Warmog's Armor and the Sword of the Divine are not as important but do help you overall.

When you are fighting with Tryndamere make sure to get the upper hand by using your Mocking Shout. Don't use your Bloodlust unless you need to because it consumes fury (the main source of you crit chance). If you need to escape or want to get a killing blow but are out of fury and are low on health, use your Ultimate. It gives you fury and makes it so you cant go under 1 health for a few seconds. After your ultimate is over instantly use you Bloodlust and kill monster in the jungle to regain you health before be ganked. Also when a turret is 1 or 2 hits from death and minion are on the other side of the map you can "Tryndamere" the turret.
How to "Tyndamere" (To do this it is advised to be 15+)
1. Spinning Slash (to the turret, this is so you can get there before it gets a few hits on you)
2. Just auto attack the turret.
3. It is dead so go kill stuff in the jungle for health.

Tryndamere is pretty overpowered, but with the build he is unstoppable.