This is my favorite Tryndamere build. As with any build it should be adjusted depending on the other team, but i find this general process works quite well with him. This build is for an incredibly dirty, powerful tryn that can out damage just about anyone. (sure thats every tryn you may say) Personally I find myself creaming other tryn's with this build.

For my runes i take armor pen marks, crit chance quints and seals, and cd per lvl glyphs.
My Reasoning:
Marks - Armor pen explains itself. With a character like tryn, who does almost complete physical damage, armor pen is a necessity. I dont take much in the way of armor pen items, so i like to have it covered with the masteries and runes. What i take gives me enough that im not too scared of armor tanks.
Seals - crit chance is super useful for tryn, especially early game. with his passive, i have enough crit chance that i dont need the brawler gloves at lvl 1. The crit chance runes give me enough lucky crits that my lane partner is usually scared sh*tless by lvl 4.
Quints - crit chance again ^
Glyphs - now you may think im crazy for taking cd per lvl, but i find that 10% reduced cooldowns at lvl 18 is pretty nice. thats not including the mastery bonuses. and if you happen to find yourself with blue buff late game? thats like an ult every minute or so. Pretty Ballin.

For my Masteries I go 24 - 6 - 0
basically everything explains itself. i put 6 in defense because i just like that small amount of mr and armor. its better than any of the other mastery points at that point. the bonus damage to minions is surprisingly nice. if you think about it, you should be killing about 100 minions per game (all depending on length of game. I've had as few as 50 and as many as 400) and 4 damage per hit on a minion ends up being quite a lot. if we average two hits a minion, thats 800 damage! holy damage Batman! seriously though, its nice. especially for lifesteal. Its not much, but early game it helps.

^i just put that tangent so this chapter wouldnt look pathetic.

Here's the important part. I start of with a vamp scepter, dont call me a noob yet, because its helps a lot with laning early on. I can usually stay in lane until lvl 6 without going back. (unless i die or get fed) If you get a pre creep gank off go back and grab a couple of pots or if your lucky, boots.
Otherwise, rush boots after the vamp scepter.
Then i usually rush PD grabbing zeal as fast as is humanly possible, and then building the rest. after your first PD you have enough move speed to get around quickly.
so i save up for a BF sword and build either Bloodthirster or Black Cleaver after PD. After whichever one you get, get the other one. At this point the game is usually over, with you either getting wrecked cause your team sucks or you suck, OR your team wrecking cause you got fed or their team sucks. (I'm not saying this build is a guarenteed win every time, nothing is)
Anyway, if the game ISNT over, grab another PD and either another Bloodthirster or an IE. A lot of people think Im crazy for not putting IE on the item list, but i actually find i dont need it. yes it makes your crit damage simply god like, but its ridiculously expensive compared to the other BF sword items, and honestly i prefer the Armor pen/attack speed from BC or the Lifesteal from Bloodthirster. And you'll be critting enough without it that it makes it slightly pointless. Without it you have 80% crit chance at level 18, and thats at full health. Tryn's passive means when you are below 60% health you'll have 100% crit. this is all worst case scenario too.

Mind you im not gonna rage if you do buy IE, its a great item and it will make you godly. If your gonna buy it dont replace the second PD, replace the Second Bloodthirster. 2 PD's means movespeed out the ********, and attack speed extraordinaire.

First off i grab Mocking shout. It took me a long time to decide what i liked the best and i decided on this because you can see when enemy champs are near you. it may give you just enough warning to get away from a gank. I see a lot of tryns taking spinning slash at lvl 1 and its not bad, but the four second slow for chases is pretty nice. also if you are in a team gank it lowers people damage so you have a better chance of surviving.
Whatever you take, remember that tryn isnt particularly scary at lvl 1 so just be cautious. Dont be useless though. If you need to die so your team gets a kill, good. Tryn isnt hard to do well with even if you feed a kill off the bat. also with your passive, your crit chance rockets as you take damage so you may be surprised at how much damage you can do.
lvl 2 grab bloodlust. max bloodlust as fast as you can so that means at lvls 2,3,5,7,9 you get it. no questions asked. Its awesome having a heal for 400 at lvl 9.

If you got your slow at lvl 1 then grab slash at lvl 4, and vice versa. you want to have all your spells at lvl 6

max ult as fast as possible. if you dont, then you shouldnt play this game.

other than bloodlust, lvl you other two spells pretty evenly. i know some ppl who max spinning slash really quickly, but your slow is really nice. take a look at it sometime. you'd be surprised how useful it is.

Exhaust ignite. Yes sometimes i find that im so much of a rapist that these seem pointless, but really they're the best there are. while tryn is not at all an aoe character (other than his slow and slash) these spells can be cast on anyone in the vicinity. so while you might be wrecking a caitlyn so fast you find it stupid to ignite her, turn around and ignite the mundo thats ulting. lol at igniting mundos. :) anyhow, i find myself doubting these spells sometimes. Exhaust is definately an necessity. in either a chase or a fight, exhaust can turn the tide. sometimes i debate over taking flash instead of ignite, but in the end ive decided that ignite is more useful for clutch kills. especially since you can slash through walls. (not sure how spinning a sword around you makes you able to go through walls but whatevs)

first lesson - BE AGGRESIVE. too many times have i seen a noob tryn look at his own health and go nahhhhhhh too dangerous. ITS NEVER TOO DANGEROUS (jk jk there are plenty of times when you shouldnt rush in) but seriously. your ult gives you 5 seconds to gtfo if you need it. but the best use of your ult is to prolong your life for 5 seconds so you can get the kill you want.

second lesson - EAT CREEPS LIKE NOBODY'S BUSINESS. honestly the best thing about tryn is how easily you can get creep fed. it gives you bloodlust stacks and that just makes you scarier. you should constantly have stacks while in lane, because that way you constantly have a 400 insta heal.

watch your cd's too. 10 seconds left on your ults cd? thats short enough for you to get in there. ( unless they've been focusing you a lot. then just wait)

Using tryn's ult - youd be surprised how many ppl mess his ult up. dont leave it too late, but dont pop it too early either. If your judgement of timing just sucks well then too bad for you.

laning - the vamp scepter off the bat gives you the ability to stay in the thick of the creep lane even at low health. At low health you'll crit more which gives you more lifesteal and bloodlust stacks, which give you more damage, crit damage, and if necessary, a heal. also dont be scared to jump your opponent(s) in lane, one lucky crit should send them scurrying.

At the end of the day (or game) i dont care what you do with your tryn build, whether you follow mine to a tee, or completely scrap it. Play your own style and if mine works well for you then good. Obviously you can mess with it a bit, but these are just suggestions.

On a separate note, jungling tryn is quite easy but you shouldnt be looking at this guide if thats what you want to do.

Finally, have fun and hope you enjoy the help with your tryn build.

Good Luck, Summoners.