I'll start by saying I'm not an expert on this matter by any means! I will always welcome the advice and constructive criticism of others. I have, however had successful results in snaring rabits in the past. As it was taught to me: use 22-24 gauge brass wire. Carefully chose a location where you can see frequent signs of your target species. (I would look for a worn path leading into a "funneled" area of brush or cover) in that funnel area, I would find a place where the tracks all converge to one single lane. A couple inches off the ground I would place a wire snare with a loop the size of my fist. I would secure the other end to a substantial branch/stick, and place small sticks around the snare to guide the rabbit into my snare. I set a few snares at a time in areas as described, and checked them REGULARLY (This was all done during winter months) I have never set a spring snare, and I was worried about a predator capitalizing on my catch, although I never had that happen.
I don't have any photos, but there are enough of them around I'm sure.
The area I currently live in does not allow the use of snares, so I'm out of practice but I don't remember it being all that difficult. The Internet and books show instructions on how to construct the snare loops, but in my experience, the location is more important that the design of the snare itself.
If I get a chance to legally practice this again this winter, I will get some photos and post them.
Good luck!