Hello, this is the way I play Tryndamere and is working after the nerf of his Q not long ago this year. Try out my build before rating, thanks. :D

My IGN: Mizukira
League of Legends Well-known Troller in SEA client! =x

Tryndamere playing Tips:
1. Do not feed unnecessarily unless it is 1 for 1 (1death for 1death)
2. Remember to use Youumu's Ghostblade's Active when chasing/escaping/farming.
3. (Executioner's Calling Active is to ensure anyone who relies on Lifesteal will perish when they 1 v 1 you!)
4. Know that your "E" can jump over thin wall, and use it to farm Jungle Minions when your lane has been pushed too much.
6. I do not own the demonblade tyrandamere skin, but, who cares if I can torn them apart like a Legendary Tyrandmere player?

How to win a game without Summoner Spell -- Flash
Easy. Just say you're level ( 1 to 11 ) < pick one and says "Oh my, I don't have my flash yet, I'm just level __ < input number below 12" and there you go! An early game victory!

Viable Marks - Alacrity, Armour Penetration, Critical Strike Chance
Viable Seals - Vitality, Resillience, Alacrity, Critical Strike Chance
Viable Glyphs - Critical Strike Chance, Cooldown reduction, Attack Damage

21/9/0

Just one point in Lifesteal for early game.
9 points in Defense to support you throughout the game.

3 points in Resistance and 1 points in Hardiness because your "W" reduces enemy's Attack Damage

Start the game off with a Brawler's Gloves and 2 HP pot.
Next, when you earn yourself 350G you can rush back to base and upgrade it to a Avarice Blade. (Not advised unless you find it really hard to last hit)
Follow up, earn 1270G to upgrade the Brawler's Gloves it to an Avarice Blade and buy a Berserker's Boot. After that, focus on upgrading your Avarice Blade to a Youmuu's Ghostblade. (You can always buy the The Brutaliser next, but remember to uprgade it to Youmuu's Ghostblade ASAP.) Upon getting Youmuu's Ghostblade, you buy your last item, Executioner's Calling.

To put it short.
Brawler's Gloves + 2 HP Pot > Avarice Blade > Berserker's Greaves > Youumu's Ghostblade > Executioner's Calling > Last whisper if there is at Least 2 Armour building TANK, if not it will be Infinity Edge > Quicksilver Sash or Banshee's Veil > Guardian Angel.

Max out "Q" first for lane sustainability and creep farm.
Next, get 1 point in "W" and "E".
Thirdly, add points in "W" or "E" whichever you like to! :)
After that, add your "R" whenever possible.

Skill Sequence for Ganking/Chasing:
"E" to jump in, followed by "W" to slow or reduce enemies AD, followed by normal attacks.
If fail, use Exhaust/"E" to jump over wall/"W" to slow or reduce AD/Active Undying rage (below 25% HP will be the best) < If you have all, use all of it IF it will ensure that you will survive! :D
(Mostly animal instinct, so, use your instinct!)

I use Exhaust and Ignite.
Viable Summoner Spells:
Cleanse - Removes CC, dmg over time spells like ignite.
Flash - Catch or Escape

Viable but not recommended for this build
Teleport
Ghost
Surge

Focus on last hitting minions whenever possible.
Try to use "Q" to heal when you have 0 fury OR only when you need to.
Instead of using "Q" to heal, it would be better to use your Healing potions to get your HP back up.
Target Squishes.
Do not think you are God-like or Unstoppable and 1v5 the enemy unless you want to lose.
Do not overextend, and participate in Gank when you know you can be more of a help then a burden.
Lastly, get into the jungle and farm the jungle creeps! (More Gold> Winning chance Up!)

Pros:
- OP Carry
- OP in Mid-Late Game
- OP in escaping with "E"
- OP in 1v1 against ANY AD/AS Champions once the core item has been built
- OP in chasing with "W" and "E" and Exhaust

Cons:
- CC will hit you hard
- People start hating Tryndamere
- You do not have a Demonblade Tyrndamere Skin

Try out this build, it is my first time making one so yeah, sorry for my lack of expertise but I hope this will help any player of any form of skills learn how I play Tyrandamere and, success in being a "Cloaked" Demonblade Tryndamere -- aka. No Demonblade skin, but Legendary otherwise. :)

Any questions do comment on the guide, and I will explain to you in detail personally! :P

Updated on Friday, 30 December 2011.
Update: I suck at making guides, though, and this "guide" is completed in 30mins