ITEM PATHING: The way I would buy my items as trynd is this:

Start with rejuvenation bead (150) + long sword (350). This will cost exactly 500, for your starting items. These build into tiamat, your first item.

DO NOT LOOK FOR SKIRMISHES! Unless ganked, since you don't have dorans blade or a general beginner item, you are severely disadvantaged lvl 1. So unless you get ganked, I STRONGLY DO NOT RECOMMEND going in for skirmishes.

Play safe, and farm out until you have 1,100 gold. This is the perfect number in which to recall with, because if you recall with 1,100 you can buy tiamat and a pair of boots. THIS IS YOUR POWERSPIKE. Tiamat deals an insane amount of damage, especially with tryndamere. So farm until 1,100 because then you can finish tiamat (825) and boots (300), so in total 1,125.

Once you get back in lane, you can look for skirmishes. However, REMEMBER THE GOLDEN RULE WITH TRYND SKIRMISHES. ONLY GO IN WITH YOUR FURY STACKED. the easiest way to do this is play back, and super safe. This will make the enemy laner push the minion wave under your tower. THIS IS GOOD. Farm up the minions to get full fury, THEN ALL IN. Likely to get you a kill.

Then you start to build the statik shiv.

Once you've done a couple skirmishes with the tiamat against the enemey laner, hopefully giving you some kills, you should aim to recall at 2,000 gold. This is so you can buy berserker's greaves (800) and zeal (1,200). Once you have this, do the same all in trick, stated above.

Then its simple from there on out. Finish stattik shiv, then build infinity edge.

SO BY THIS POINT YOUR BUILD SHOULD BE: Tiamat, berserker's greaves, stattik shiv and infinity edge.

Then build Blade of the ruined king.

Then, build you last item, either GA, Frozen Mallet, Deaths Dance or Sterak's Gage.