[1] Bloodlust is the first and most important ability of [2] Tryndamere. Not only does it increase your sustain in lane, but it also deals attack damage in depending on your missing health. In short, the less health [3] Tryndamere has, the more damage it does.
Due to its passive effect, [4] Bloodlust pairs well with [5] Undying Fury, which prevents it from dropping below 1 health, giving it a huge bonus to its attack damage.
The true strength of [6] Spinning Slash is in its utility. Aside from dealing damage, it allows [7] Tryndamere to walk over enemy units and terrain, including walls and turrets, making this a very useful ability.
If you're running low on health, go to a wall and go through it. The longer it takes your enemy to cross it, the better. But if you're stuck in an open field where you can't get through a wall, turn anyway, as it will put much more distance between [8] Tryndamere and his pursuer.
If you have no chance of escaping, sometimes it's best to turn around, activate [9] Undying Fury, and attack your pursuer, especially if you're alone. If they turn around and run, press down and keep using [10] Spinning Slash to close the distance. With luck and good items, you will be able to at least kill an enemy Champion and possibly survive, this is much easier if your team helps or the enemy is separated.
[11] Spinning Slash can be a great offensive weapon, if used correctly. Thanks to its fast cast and range, you can use [12] Spinning Slash to position yourself, initiate ganks, and catch up with escaping enemies.