Hi! This is my second build and I wanted to post a more survivability focused build for Tryndamere. After the update, I feel that tryndamere was buffed in crit percentage without relying on his ulti, Undying Rage, too much. This is yet another work in progress, but hopefully it helps you when playing Tryndamere he's so much fun.
Enjoy. :)

Here are some of my past games.

PROS:
+ Great DPS
+ Awesome ulti
+ ALOT of damage (Especially after Infinity Edge)
+ Great juker...really, it's pretty fun juking the other team.
+ Insane crit percentage and damage.
+ Fun
+ Make people rage/rage quit

CONS:
- BEWARE OF THORNMAIL!!!!!!!************
- Pretty fragile
- Easily focused
- Useless if caught under heavy CC
- One trick pony :(
- Ignite and damage over time skills will screw you over.

I go with exhaust/flash. I know exhaust seems unnecessary but it works when there are other heavy damage dealer's and you can slow and reduce incoming damage for a bit.

You could also use cleanse/flash, ignite/flash, or exhaust/ignite (wouldn't recommend this unless you're just absolutely certain you won't be killed much.

Okay, so I know most of you think loading on crit runes for Tryndamere is a must. However, actually after the changes that were most recently made, Trynd gets plenty of bonus crit chance through his rage. Now, the only important part would to be maintain full rage as much as possible before engaging.

That being said my rune setup is actually the same as Phreak's rune setup in the Tryndamere Champion Spotlight after the changes were made. I tried many variations and this seems to work best for me.

I prefer lane Trynd and go with 21/9/0 mastery setup. The offensive page is pretty standard crit focused and the defensive page I put 3 in increased MR, 2 in increased armor, and 4 in dodge. Trust me, there were many times when dodge has saved me.

As Tryndamere, you want to farm as much as possible. The reason behind this is because his build requires alot of expensive items and the sooner you can manage to get them the better. By the end of the game I average anywhere between 140 ~ 200 creep kills. Grabbing red buff as much as possible is also very useful when going for kills.

Alright, I actually dread jungling as it is boring and hardly any action going on, but there are always those teams that will cry all game about how you fail because you didn't jungle. So, if you must here is my jungling section.

I grab vampiric sceptre first and start at wolves. I then proceed to wraiths where I smite the blue wraith and autoattack the rest. Next, I got to the twins. After killing the twins I usually return to base to get a cloth armor and one health pot. I then go to blue golem and get blue buff. Afterwards I will do wolves, wraiths, and twins again. Return to base to get your boots. You should be level 4 or 5 by this point and I usually stop my jungling here. I will go around ganking wherever needed and afterwards if possible I will take out dragon. You're Wriggle's Lantern should now be finished and it gives you one free ward to use. I will grab a couple more and start warding. I won't get into warding because there are plenty of videos and warding guides. :)

Laning:

I found that when starting in the bushes spinning slash is better in that i start with vampiric sceptre and if done right you'll be lifestealing everything back. It also helps chase down that annoying champ that flashed away. So basically, I get this in hopes of getting first blood or to have them waste their flash and have them go back to base. Starting level 2 I max out Bloodlust first. This is kind of a must. I grab my ult whenever possible and I max out Mocking Shout second. The slow is much more useful than the spin in my opinion. Finally, I max out my spin. Spin to win?

Jungling:

I start with Bloodlust and max that out first while jungling. I grab Spinning Slash at level 2 and max out Mocking Shout second. Of course, ulti whenever possible.

Whether laning or jungling I end up with the same core build. This build consists of: Berserker's Greaves, Youmuu's Ghostblade, Phantom Dancer, Bloodthirster, Infinity Edge, and Guardian Angel.

Berserker's Greaves: I get these because I rarely get to the point where I buy another Phantom Dancer.

Youmuu's Ghostblade: This item is the ****! It has the increased attack and movement speed (great for chasing or falling back), It has enough armor pen, and it also gives CDR. This item has helped so much for kills, juking, and backdooring.

Phantom Dancer: This item is your main source of attack speed and crit percentage. Not to mention it gives a nice amount of increased movement speed.

Bloodthirster: In order for your crits to hurt you need the damage.

Infinity Edge: I feel that this is a must for crit champions like Trynd, GP, AD Shaco, Pantheon, etc. This is what makes Tryndamere a brutal killing machine. At full build, expect to crit 1200 damage. It's beautiful but EXPENSIVE!

Guardian Angel: I only just recently started doing this with not only Tryndamere but most of my melee dps champions, but I found this best helpful for Tryndamere. Why? Because with this you have to kill him twice pretty much.

Phantom Dancer (again): I usually never make it this far, but I just had a 82 minute game the other day.

Elixirs: I just buy these for the little boosts after I've completed my build. Oracle's Elixir, however, should be bought whenever possible to find and destroy enemy wards.

Mercury Treads: I always get these boots when going against a heavy CC or pain in the *** CC (i.e. stuns and snares).

Atmogs: Sometimes there is a need to build more tanky.
(This plus the Guardian Angel makes you a royal pain in the *** offtank.......and just in case some people newer to League don't know that would be Atma's Impaler and Warmog's Armor)

This is pretty simple.
1) Wait for the tank to initiate and let some CC be cast.
2) Spin in and attack squishiest to tankiest and don't forget to cast Mocking Shout when enemy team is running and they are in range.

*Somewhere after you've engaged in the fight it would be nice to use your Youmuu's or use it when you've been affected by CC to get that really low guaranteed kill. It's really up to you.

During ranked games I strongly suggest you lane with a champion with a snare or stun effect as that's going to ensure some of your early game kills. Please do not think you are invincible as Tryndamere in ranked. I mean, it's ranked! Alot of them know every which way to counter you if you do anything too daring.

Well, I'm not sure if my guide is nothing anyone hasn't said before or if it will be helpful at all. Tryndamere is a nice DPS champ to have on your team but then your team also has to be able to cooperate at an experienced level. But then again that's for any champion. Don't feel bad when other players rage/rage quit because you're quite capable of atleast a quadra kill and you have 20+ kills. That's kind of a joy of playing Tryndamere. Well gl & hf!