A snare is basically a slipknot. The goal is for the animal to walk through the loop, and as they walk through it it tightens around them (usually their neck, sometimes their abdomen depending on the animal, sometimes the feet depending on the trap), and then by struggling to get out of it they make it even tighter.
For a basic snare trap, simply anchor the other end of the snare wire to something strong enough to hold a struggling target animal and suspend the loop where you want it. Height, size of the loop, and placement all depend on the target animal.
In this case (when I test the guitar string in the next couple days), the target animal is rabbit and so I want the loop to be about 6" in diameter, the bottom of the loop about one hand's length from the ground, and the sides to be a fist's distance from any obstructions (like bushes). Because this is a bottleneck with thick brush and a sapling around it, I can anchor the snare to the sapling and hang it in the opening between the brush, suspended by some twigs or something.

I have a PDF about traps in my big file directory of everything survival-related if you want it... covers everything from basic snares, to deadfalls, to fish traps.