Now before we go any farther I need to say one thing that you should remember for the rest of your life (but probably won't, actually please don't, but keep it in mind for this game).
Tryndamere is NOT a tank!
Ok, ok, I know, there are beautiful Tryndamere tank builds, and they work. Very well actually, but they are SLOW
So for the purposes of this guide, Tryndamere is not a tank and you should not build him as one. That being said, you will be targetted a lot, in fact you will rush in and invite people to hit you as they notice the large dps you are generating, and guess what? you want them to be hitting you, you better be getting hit a lot or you aren't playing the Dark Champion to his full potential.
But wait you say:
Isaic you are confusing me. You just told me that Tryndamere is not a tank, but now you want me to provoke attacks, rush in and get focused fire.... That's a tank's job!
And that is why Tryndamere is such an awesome hero. You can build him pure dps and you are better than a tank at soaking up damage... at least for 7 seconds, but I've tarried long enough. Lets get into the nitty gritty details.
These are Tryndamere's skills
More info on the abilities, friend~
Passive: Whenever Tryndamere kills a unit, he gains 4% increased critical chance and 8% attack speed for 15 seconds (stackable 2/4/6/8/10 times.)
Active: Tyrndamere consumes his Bloodlusts, restoring (Edit: now the first charge heals 130 HP) 65 (+AP @ 4:1 Ratio) health for each.
W: Mocking Shout
Decreases surrounding champions' Physical Damage by 20/40/60/80/100, and enemies with their backs turned also have their Movement Speed slowed by 30/40/50/60/70%. Lasts 5 seconds.
E: Spinning Slash
Costs 30/60/90/120/150 Health
Tryndamere spins through his enemies, dealing (Edit: now 110/150/210/270/330) (+AP @ 1:1 Ratio) Magic Damage to enemies in his path.
R: Undying Rage
Tyrndamere becomes completely immune to death for 7 seconds, being unable to be reduced below 1 health. Also applies Bloodlust 3/6/9 times.
At level 18
0 Ability Power
Lvl 1: Bloodlust/Spinning slash (depends on whether you are solo or with a partner. Slash for aggressive early play, bloodlust for defensive early play)
Lvl 2: Bloodlust/Spinning slash (depending on which one you didn't get before)
Edit: People have been pointing out to me to remind that spin is a great way to escape and chase, it can go through impassable terrain, so though i recommend only 1 level of spin early for this build, its a vital skill to have
Lvl 3: Mocking Shout
Lvl 4: Mocking Shout
Lvl 5: Mocking Shout
Lvl 6: Undying Rage
Lvl 7: Mocking Shout
Lvl 8: Bloodlust
Lvl 9: Mocking Shout
Lvl 10: Bloodlust
Lvl 11: Undying Rage
Lvl 12: Bloodlust
Lvl 13: Bloodlust
Lvl 14: Spinning Slash
Lvl 15: Spinning Slash
Lvl 16: Undying Rage
Lvl 17: Spinning Slash
Lvl 18: Spinning Slash
Start off with health regen, I'm not saying which one (just not a Doran's). I like regrowth because I like to get aggressive and stay in the fight longer, but the beads has a plus because you can more quickly get your mid items and thus your late items.
Mid items: brawler's greaves and optional avarice blade. The attack speed from the greaves are absolutely necessary and the crits are nice for... well you'll see
Late item: Infinity Edge is epic on Tryndamere, nuff said. 250% Crits is not a puny fact when you realize that tryndamere is going to be critting more than normally attacking late game. From bloodlust to his passive, Tryndamere is meant to crit, you will be doing insane damage, and nothing else comes close.
After that, this isn't necessarily a core, but Phantom Dancer adds more crit, attack speed to take your dps through the roof, and adds movement for chasing and dodge to keep your hp out longer before you need to ulti, what's not to like
(notice any Tanky items? I don't think so. And don't give me any of "Guardian Angel is a tanky item" bull)
Spells: Ghost (very good), Exhaust (optional, can replace with boost, blink, etc. Whatever purpose you need to fill). I like these two because ghost is both defensive and offensive oriented, and you'll need that extra speed as your ulti is running down. Exhaust is good because i like an extra snare to go with my mocking call, which will from now be known as the chicken call.
None of this is necessary mind you, I've been able to get to huge kill numbers each game without any runes/masteries when i was low level
Masteries I like to go pure physical damage in offensive, and indifferent between the other two
so either 21/9/0 or 21/0/9
Runes go for hp regen which good early game, and damage/attack speed/critical, anything that goes into the damage formula. I like movement speed and cooldowns also.
By now you have figured out the reason Tryndamere should be asking for punishment is because of his ulti, and his ulti makes him the best mindgame hero currently within LoL. If your opponent has even the slightest morsel of greed in his soul (and knowing LoL/Dota players, that's like saying "if politicians ever fail on their campaign promises") they will become your prey
Great thing for you, it doesn't matter what lane you are in. You can handle solo or dual, and both will leave you well off. People looking at me askance for saying you can handle solo (yes dual disablers will rape all solos) should be pacified when i say handle solos defensively and with care, at least until level 6.
If you are solo, just last hit and bloodlust whenever your health drops below full, the new bloodlust buff which lets the first heal 130 makes this strategy extremely viable. The trick is to seem a worse player than you are. Don't even spinning slash anything, your base physical damage should be all you need if you are halfway decent at lasthitting, if not practice makes perfect.
When you hit level six, make your life gradually go down by giving them opportunities to harass you. Get them to push near the tower, and run to hit them when your life tells both of you that you shouldn't. Most likely they will take the bait and hit you or even better start chasing you (run back a little to give them a chance to do this. Turn on undying rage (be careful when, you don't want to do it too early, but some heroes have nukes, so know your enemy when you time this) And hit back. As they realize, albeit too late that you are unkillable, they will now be taking your attacks and the tower's damage and your hits, and ooooh how they will run
and BOOM you hit them with mocking call (AKA Chicken call), yep those damn chickens will feel shame to their bones and be slowed, guaranteed kill, but probably by the tower. You shouldn't chase in case undying runs out and their partner owns you. after undying ends, use up the lust counters it provided and just go back to laning. None of this actually has to happen for early game to go smoothly, you can just farm and not die, and thats a success.
If you have a partner, depending on your play, you can be offensive with slash and mocking call, or just farm. Undying rage also has offensive capabilities away from the tower, also relying on the opponents greed as they think they can kill you before effecting their escape, leading to them dying and you running away with one health. Otherwise, the play is same as solo.
Got your boots and maybe an avarice blade, and your job is now to just constantly be on the move. Last hit a wave, kill some creeps, but your goal is to hunt for oppurtunities to interfere in fights. Gank with mocking call and help your team kill. Your one level of slash gives you great mobility to get into call position, remember it only works if they are facing away from you, and even without hp items you have decent life to take some hits and dish some back out.
Your other role is bait. If the teams are not fighting, get the enemy to chase you by letting yourself get disable and taking some hits. Run into the middle of your team and then start hitting back. turn on undying and then enemy will be wasting their hits on you, while your allies will be not so ineffectually pounding back. If they run, remember you have that awesome, awesome snare that reduces their running speed to that of chickens. Learn the undying rage timing and ghost out just before undying ends (using the lust charges of course)
Your main goal is to keep your towers intact at this point in the game, don't worry about kills, that comes after you get your infinity edge.
You got your infinity, and you are now a dps monster. Just continue doing what you were doing mid game, but now you are going to be taking out a good 2 or 3 champions out average in each team fight. Don't be intentionally going for one on ones, Tryndamere if you haven't noticed is a team player. Midgame he gets other player kills by distracting and slowing the enemy for their hits, now he relies on them to stay around him to disable/slow/tank/distract/etc. to let him do his work.
That's not to say you still aren't going to attract hits. you still want that because the lower the hp Tryndamere goes, the faster the crits come. Even behind in level, tryndamere with or without support can own other physical dpses because 7 seconds is such a long time.
And here is where the unbreakable glass comes in, imagine a champion that deals 400-500 damage with every other hit and can slow you, so you can't escape, and no matter what, you can't be rid of him for at least 7 seconds. Now that is a nightmare...... if you are on the other team.
That's not to say you want to be constantly living on the edge. Remember to keep your head and know when to be aggressive and when not to be. The best way to do this is experience, you'll learn what opportunities are golden and which are just greed pits of doom. This applies to every hero, Tryndamere just allows you to be more aggressive than usual.