How to use Transect-based sampling to select sample trees
More detail on what your studying, the question you want to answer, and how you want to go about doing it would be very helpful. But I can answer this basic question of how to select tree's with a transect. 

You will need:


Forms to fill out for data.
A compass.
A transect tape (really a very long tape measure, about 100 yards or meters).
A sampling design that fits your study. (I'm assuming you already have this, but if you want to talk more about it see above.) 
A wooden meter stick. 


Once you are in your 1st area and ready to select a random subset of trees. 


Pick a random spot. (Usually done by throwing a stick or water bottle over the back of your head and going wherever it lands).
Pick a random number between 0-360. This will be the random direction you go in from your random spot. Find north on your compass, then which way your random number points. In your mind mark a way point in that distance you can walk to (a mountain peak, a distinct tree, anything).
Stick the beginning of your transect tape in the ground and start walking. The length that you walk should be predetermined from your study design. 


Now you'll select trees to perform whatever measurement that you've decided on. But how? Most forests are not so dense that a straight transect tape will touch many of them. This is where the meter stick comes in. Walk back down the transect and choose any tree that comes within 1 meter of the tape on either side. Is the forest not dense enough to include enough trees that way? Then simply increase the length of your transect, or length that you measure out from the transect (ie. 2 meters, or 3 meters). 

This is technically called a "belt transect". And it used in natural resources to measure things that are abundant, but not very dense. Such as trees in a forest or shrubs in the desert. It is essentially a giant quadrat.

Why all the randomness? Humans are naturally bias. Even if you think you are not being bias, you could subconsciously be choosing a starting point in a dense patch of trees, or a direction that will let you measure your favorite species. A rigorous study relies on a random sample of a population of interest, and small non-random decisions like this means it is not a random sample, but a bias sample.