Tryndamere has pros and cons to work with.

Pros:
Extremely High damage out put.
Ultimate that makes him not able to die for 5 seconds.
The ability to use that Ultimate even when suppressed.
A slow with Mocking Shout.
A speed up with Spin.
Laneability with Bloodlust.

Cons:
Easily Harassed.
Slow swing speed means missing last hits on minions.
little chance to harass other players.
Countered with a high HP champion with Thorn Mail (Like Rammus)

Hello,
Tryndaspindawin is a very easy champion to work with. His baseline is so high that he requires little to make him useable at any elo. It is the reason why Tryndamere in Indonesian means "Easy Warrior." This is going to be a very quick little guild on what works with him.

Most people will try to critical strike with Tryndamere, which is very important, however, Tryndamere is more then a critical machine. I will explain why I take each after. For this reason the runes I take are:

9 Marks of Desolation
The early armor penetration makes Tryndamere a laneing nightmare. After spinning up early game he bypasses most champions armor with only the 9 marks. This also works later on in your favor when champions gain more armor, as it still passes right through much of it.

9 Seals of Alacrity
Since the revamp of Tryndamere, including the rage system, he gains rage off of hits, not just critical strikes like the bloodlust stacks did. This makes the ability to hit more, as opposed to hitting harder, very important. Tryndamere does not have a fast attack speed so he needs help. It is easy to lose some last hits on minions because of the amount of time it takes to swing.

9 Glyphs of Warding
Warding give the magic resist Tryndamere needs to stay in the lane against a pushing and harassing mage or support. Tryndamere major downfall is that he gets harassed easily early game and it can cost minnions, last hits, and deaths if you are not careful. The warding gives you minor protection against mages and can allow you to survive a nuke if it's cast in your direction.

Quints of Alacrity
Same reason for using the quints as using the seals. Tryndamere has a slow attack that hits hard. The boost in attack speed is very important.

Tryndamere is a DPS AD champion. His masteries should complement this. Since he has no need for AP or Mana, head down the left side of the offensive tree. 21 offensive masteries gives Tryndamere a huge step up on anyone who wants to try to use the defensive tree as a base. The 9 in he defensive tree are based around gaining armor and a little bit of magic resist. Since you have the runes for Magic Resist, it is a good idea to have some armor. This will help against minions and other AD champions.

For starting items I choose a dagger and as many health potions as I can get my hands on. As quickly as it can be done I turn it into Zeal. The reason why I go directly to Zeal and not to Berserkers Greaves is because Zeal gives Tryndamere movement speed already. It also gives him critical chance, and the ever so important attack speed.

After that I up my movement a little bit more with the Berserkers Greaves. The attack speed mixed with the movement speed makes anyone hard pressed to just run away from you. With the spin, mocking shout, and items, getting the upper hand on another champion becomes easy. Even more so when they have no escape.

After I have attack speed and movement speed locked down, I grab some sustain. A simple Vamperic Scepter gives the health restoration I need to not have to waste my rage on healing every time it fills up. At this point you've spent around 2.4k in gold. This is cheap in comparison to other champions who require Rabadons Death cap or Warmongs to survive past level 6. Unfortunately, it cannot stay this way.

The only really expensive item you'll need is the next one: Infinity Edge. Infinity Edge gives Tryndamere the edge against any champion at this point. Level 6 with endless rage and an Infinity Edge means you are hitting hard, fast, for 250% damage, and gaining it back from the Scepter. After that you round out the build.

Tryndamere turns the Zeal into a Phantom Dancer and let the light show begin. At this point you are swinging for the fences and hitting like truck. The Phantom Dancer will also make it even more difficult for any champion to get away. Farm out jungle, gain money faster, kill minions in a single hit, and take out towers.

Tryndamere turns the Scepter into an Executioners Calling, using the greavis would ability when ever possible. It rebounds every minute and not using it is a waste. It ups the critical chance, and life steal that you had so going into a battle without rage is less of an issue.

This next item is very near and dear to me as Tryndamere. Frozen Mallet is a life saver. The 700 health and slow on attack means no one is getting away from you. It procts on spin so when spinning into a crowd, they all slow down. The health makes you more tanky for late game so mages cannot burst you down before you rage, if only you had some armor...

Atma's Impaler fixes that. This rounds out Tryndamere's rageless critical chance to 88%. It gives armor and more damage to make Tryndamere's critical hits harder and you more survivable and in the late game when mages do 10k damage to anyone who has no MR and other AD's do 500/second to anyone unarmored, isn't it nice to know you out damage them, out hit point them, and have more armor and MR?