Use a snare - they are really easy. Just stake one next to a run and set up a 6" loop in the run. I use 3/32" cable and 4' of rebar hammered into the ground as a stake. Use a long stake because beavers are STRONG.
I'll just add to make sure to use an anti-reverser so the tension won't back off and use aircraft cable as with solid wire of too small a gauge they can spin and snap the cable.
Bodock is 100% right, they are really strong the buggers.
I am headed out in 10mins to say goodbye to as many as possible.
