base information
tryndamere is a true damage dealer and pretty hard to kill thx to his ulti. but when playing tryndamere you need to choose when you are on low hp between: stay and fight for major damage or get back heal a bit and get back in or in worst case senerio recall. i usually go with the second so i wont die to fast but still deal quite some damage.

spells
i go with ghost and ignite to make sure i get the kills and be able to escape without to much trouble you can use ghost for both. ofcourse you also have spinning slash and mockingshout to get kills or escape so other choises could be cleanse, teleport, clairvoiance or maybe fortifie or smite. however the spells realy depend on your playingstyle. if you like to be defensife and dont lose the turrets all the time you would take fortify i guesse but if you are sure you can pull it of (however i dont recommend it) go jungle with smite and more to pick.

abilities
i take an early point in spinning slash for the manourvebilitie so i can get away or go in easely bloodlust is my main abilitie since it heals you when you activate it and gives you bonus damage when you keep the stacks. mocking shout is my "second" abilitie so i can catch up with fleeing enemies or reduce damage of enemies like xin or yi. ofcourse i want to lvl my ulti as soon as possible too since it is the reason why tryndamere is a great champion.

masteries
always take the offensive tree with tryndamere it will realy help earlygame and also be of use late game with the 5% increased damage. and the offensive tree is actually the only "good" tree for tryndamere since you dont need the defensive one because of your ulti and the utility one is for casters but tryndamere doesnt realy need his abilities but it is realy nice.

runes
you can go two main ways here. you can go crit damage or crit chance. i go crit chance so i can buy damage items in game but if you want you can get crit damage runes and buy some more crit chance in game. again this depends on your playing style.

items/in game guide
early game
i start of with brawler gloves for a good crit chance for first blood. then i get avirice blade and beserker greaves mostly at the same time around lvl 4-6 wich depends on the game development. if you should play offensive or deffensive depends on the enemie and if you lose or win the lane. so what to do is up to you.

mid game
around here i get infinities edge and phantom dancer. this also depends on the development of the game. and make a start with bloodthirster.

late game
here you should be half way bloodthirster of starting black cleaver. now its about knowing when and what to do. know when to attack, when to defend, and when to be passive and just keep it as it is. this is obvious but i see quite some players that make wrong choises based on beeing greedy or wanting to much to soon.

and remember "its not about winning its about having fun :D"