Welcome felow summoners xD

Good farmer, good aoe damage, more tanky, and better burst damage output the tryndamere AD at begining, every skill counts to lich bane like mocking shout, bloodlust even his ulti, so take advantage from that, jungle is possible just use 5 health potions and a hunter´s machet and it´s a fun way to play tryndamre.......( hey at least for me xD).

Not a good dealer damage as Tryndamre AD in mid and later game, after spinning slash even if it is an aoe skill you must take max advantage of your lich bane then, people will always rage at you for seeing an tryndamere AP so make sure to ask if they can choose as least 2 AD then don´t say you go AP xD or you never start the f.......(censored xD) game.

For spells i take flash for fast and good position of yourself either a defense strategy of a offensive one, ignite for and extra tool damage for killing others when the enemy has lower hp or for cutting the regeneration that some champs got like doctor mundo and fidlesticks, and also for the extra 5 AD and AP if you put 1 point in summoner´s wrath on masteries.

I first take Spinning slash as it is you main damage and first priority to max first, then bloodlust as second priority because of the heal and the ad it gives is always nice since that attack bonus helps also your spinning slash, for third again spinning slash for more damage and the mocking shout is at last because is used more as a tool on Tryndamre AP and undying rage is a must have whenever you can not only that gives 5 seconds of you being imortal, but more because of the lower cooldown it receives.

In greater marks i choosed mark of armour penetration over mark of magic penetration because spinning slash is a skill that takes advantage from both AP and AD items but still an AD skill, it´s your main damage so since it is an AD skill there´s no point using mark of magic penetration runes at begining of the game just would help later because of lich bane.
Greater seals i choosed seal of armour runes for helping at begining against AD champs.
Greater glyphs i choosed glyph of ability power since it boosts your spinning slash.
Greater Quints i choosed quint of ability power to boost spinning slash and helps to put more damage to auto attacks thanks to spellsword masterie and lich bane item if you wish you can choose quint of armour penetration it is also good since spinning slash is an AD skill and helps better your basic attacks.

I put a lot in the offensive tree taking as much AP damage and armour penetration i can get, since your spinning slash is your main damage, the armour penetration will help a lot to give more damage and to trade some basic attacks better, cooldowm helps to reset spinning slash faster, at begining Arcane knowledge will not help but when you finish the Lich Bane it will help; executioner well is a must since 5% more damage you will deal for just 1 point; now to the defense tree i take durability since HP is always a good friend.

As you can see i take the most AP as i can get reaching as fast as i can to lich bane first then boots and after rabadon's deathcap for more damage.
After that i focus on more Life the slow thatt rylai's crystal scepter is greaaat since your skill is also an aoe damage yeeees xD it takes advantage from that in team fights, after some cool down reduction with some attack speed to help trading faster the hits from your lich bane also and remenber you got a good armour penetration from runes and masteries,then the if the game has not ended yet go for more survival items like the zhonya's hourglass and runic bulwark.
You can choose to buy oracle's Elixir anytime if you see the team needs some ward harras or teemo mushrooms, but that´s suport job most of the times, and heeey don't forget to buy the f....... elixirs they are cool for the comunity xD and both are good also since spinning slash take advantage from ad an ap remenber.

And that´s it a simple guide i know it could be better, but i wanted to make as simple as i can do for the ones who maybe will read this, before you say it´s a **** there´s always a way to play champs in other forms, like master yi AP, Tristana AP even Rengar AP xd if you didn´t see at least one of these as AP you are a noob xd just joking, give it a try just that, remenber spinning slash is an AD skill that takes advantage from AP its not like the Q of master yi, well just have fun people try be diferent it´s nice and cool way to try tryndamere.