Phishook

Before you do anything, Check the laws in your state on beaver.
In Maryland, it is illegal to shoot a beaver. It's, also, in 7 counties illegal to use a snare.
Beaver are fairly easy to trap. I use a no.#4,mb650 or mb750 leg hold attached to a drowning cable with a one way slide. That is the easy part. It took me over 2 hours to skin, flash and stretch my first beaver. Find a local trapper. Most will be willing to help you. [ If you don't know of a trapper call your D.N.R. they can help you find one.]
I'm a Nuisance Wildlife Control Cooperator, Hunters Safety Instructor and a Natural Resources Police Reserve Officer in Maryland. And I do hunt and trap. No way would I shoot a beaver in or near water. Not only does it damage the hide. But it is very dangerous. Bullets will ricochet off water. A 22 bullet can travel over a mile. A higher powered rifle? who knowns? You may hurt or kill some one.
Safety First!!!