Bloodlust is Tryndamere's first and most important ability. Not only does it increase your lane sustainability, but gives you more attack damage plus a bonus in accordance to your missing health. In short, the less health Tryndamere has, the more damage he deals.
Spinning Slash's true strength lies in its utility. In addition to dealing damage, it allows Tryndamere to pass through enemy units and terrain, including walls and turrets, making it an incredibly useful ability.
If you're running low on health, head toward a wall and spin through it. The longer it takes your enemy to walk around the wall, the better. But if you're caught in an open field and can't reach a wall, spin anyway, as it will put more distance between you and your pursuer.
If you have no chance of running way, it's sometimes better to turn around, activate Undying Rage and attack your pursuer, especially if they're alone. In-turn, if they start running away, press the assault and keep using Spinning Slash to close the distance. With luck and a proper build, you'll be able to kill at least one enemy Champion, and possibly even survive, if either your team helps or your enemy was alone.
Alternatively, Spinning Slash can be a great offensive weapon, if used correctly. Thanks to its rapid casting time and range, you can use Spinning Slash to position yourself, initiate ganks, and chase down fleeing opponents.
Spinning Slash is also effective against minions, as it damages multiple targets at once and generates more Fury for Bloodlust. The more enemies you spin through and kill, the more Fury you'll get.
If you're taking down a weak enemy tower and see an enemy Champion moving toward you, you can use Spinning Slash to both run away and damage the turret even further. With proper timing, you'll both destroy the turret and put some distance between yourself and any possible pursuers.
Mocking Shout is Tryndamere's debuff ability. Although it doesn't help deal damage, it still has its uses, as it automatically effects enemy Champions within its radius without needing to be aimed.
Keep in mind that Mocking Shout always reduces the enemy's attack damage, regardless if the slow is applied or not. This makes it an excellent ability to use in a team-fight. In addition, it can also be used during the laning phase to decrease an enemy Champion's attack damage ―causing some of their last hits to fail, if well timed.
Mocking Shout is an excellent anti-jungle/ganking tool, as it doesn't need to see an enemy Champion in order to affect it. If an enemy Champion is hidden, but within range, the ability icon will go from grey (unusable) to colored (usable). This can be very effective when walking through an enemy jungle, allowing you to gank enemy players.
Undying Rage is what makes Tryndamere so deadly. Though the invulnerability period is short, the few seconds it buys is sometimes enough to turn the tide of battle. Try to delay its activation as long as possible, as you can still lose health while it's active. Delaying it is also a very effective way to cause an enemy Champion to over-commit to killing you. It is, however, always better to activate it a moment too early than a moment too late ―while both can lead to your death, the former reduces the chance of being killed by a high damage burst.
Undying Rage's offensive application can be used to devastating effect. In addition to making you immortal, you'll receive a massive boost to your current Fury upon activation, drastically increasing your critical strike chance and overall damage output. Ideally, you'll want to be in melee range when you activate it, so you don't waste time chasing your opponents. Even if you don't kill your opponent, Undying Rage can force them to retreat.
Undying Rage also makes Tryndamere an excellent one-on-one dueler, as his high damage output can demolish enemy Champions. You can also activate it whenever you're being chased in order to turn the tables, and possibly even kill your pursuer.
Even though Tryndamere does not need to purchase a lot of defensive items thanks to his ultimate, you may still want to build at least one defensive item on him. This is because his ultimate may not always be avaliable for use, and the defensive items may have some utility of their own.
The best item in this case is Guardian Angel. Tryndamere is already extremely hard to kill on his own, and generally tends to attract all of the enemy team's CC. With this item, however, they must think twice before doing this if Tryndamere has his ultimate avaliable, since Guardian Angel will ensure that he will kill any target or escape with life.
During laning, Tryndamere is vulnerable to ranged harassment. If you can manage to keep him from last hitting, you can deny him his heal along with gold. Just be careful; some Tryndamere players have full Rune pages for crit chance and crit damage, which makes him deceptively strong at low health. Also, be wary, as he can quickly use Spinning Slash to close the distance and deal damage of his own.
Although Champion and Champion ultimates do not kill Tryndamere or prevent him from activating Undying Rage, suppressing him during his ultimate effectively wastes its duration, and with proper timing you may be able to kill him after his Undying Rage runs out as the suppression does not allow him to escape or heal, while their ultimates will still be doing damage. Both playing and countering Tryndamere is all about timing.
If you are a tank, are being focused by or have a lot more health than Tryndamere, Thornmail can be used quite effectively against him. By having 30% of his damage returned to him he will quite literally be killing himself if he cannot kill you quickly and will most likely be forced to use Undying Rage earlier than he would like to. Getting a Randuin's Omen or Frozen Heart will however be more useful for your team, as they can decrease Tryndamere dps through the attack speed slow.
Hemoplague is an excellent skill to finish off Tryndamere due to the 5 second delay. However, it is not recommended to waste Hemoplague on Tryndamere if he is alone. Using it during a team battle after he uses Undying Rage will almost ensure a kill.
Death Mark is also effective at finishing him off, but make sure to wait 3 seconds after he uses his ultimate. Otherwise, Tryndamere will still survive.
As a carry, Exhaust is extremely effective for countering him, since his damage comes almost exclusively from autoattacks.
Tryndamere excels at 1v1 fights. Ensure you are in a good position to give yourself an edge before committing to the fight. Be careful even when at your turret as it may not kill Tryndamere while his Undying Rage is in effect.
If Tryndamere attempts to turret dive you, run away and juke him until the duration of Undying Rage wears off.
Tryndamere is centered around intimidating opposing players to over commit to highly disadvantageous situations and make bad choices. In particular, Tryndamere excels at chasing fleeing enemies. Experienced Tryndamere players know this and usually attempt to use his abilities to intimidate an opponent into fleeing; which almost guarantees him an easy kill.