I see you had over 90 views, but no replies, so I'll try and help.
I trap and snare beaver... but really like to snare them not only because it's fun, but it works.... very good too.
I like to use cable size 3/32" 7x7 galvanized cable in snare lengths from 40" to 7ft. I use a special locks designed just for beaver and also other, but suitable locks.
I find spots where they naturally travel, but they can belured to certain spots where they can be ambushed by snares... or traps.
I can write a lot here, so I'll only address one option...
Find a spot where the beaver is naturally swimming and set a snare 8 1/2" to 9" across 1/2 into the water. Anchor snare to something solid that won't move or can be chewed off... like a root or small tree. Snares can be anchored just like traps too... with a trap stake. They can also be anchored with something called an earth anchor or disposable stake.
You will need a seperate wire in the #11 or 11 gauge size. Others use different sizes, but #11 works for me. It's black and it's called annealed wire located at most hardware stores... but you most likely won't find that gauge wire there, so you may have to double up #14 gauge by twisting it together for more strength. This wire is called the support wire and is used to hold the snare into the correct position and height. It can be twisted to a nearby stick or even twisted onto a stick then the stick is poked near the snare. The wire only needs to be about 10 inches long and attaches right behind the open snare loop just behind the lock.
Sorry, I can't write more, but it takes time to properly try and paint a picture of what I'm talking about! If you can figure some of this stuff out... great! Snares are an excellent way to trap beaver because if you miss them, they won't get snare shy as they will never know they just missed snare!
Good luck,
Snareman