Never got a chance to trap beavers, but I think it would be an adventure. I'm sure there are great books that detail trapping those pesky creatures along with tips you get here. Beavers are very interesting animals and I love to watch them from a deer stand along a swamp but they do some major damage with water levels and flooding not to mention tree felling which they seem to do for recreational fun. Good luck on the trapping.
Just passing on some info that i learned from others/reading. The easiest way to trap beavers is to find a shallow channel they are using or a spot that they frequently use to exit the water. You can use a #330 body gripping trap using sticks jammed in the mud to funnel the beaver through the trap. These are some powerful traps so you should be careful setting them. Also look into handling the fur first so when you do get one you know what to do. I'm getting ready for next years trapping season. I am planning on targeting mink and muskrat so I can get a good feel for processing the fur.
There are many types of traps as well. One keeps them alive and well and another just acts like a mouse trap...wham. As timetohunt said using a channel works well and you can also make a trough in a dam and allow water to go through and set a trap where the beaver will be going to make repairs and just make sure you anchor the traps well so they don't get carried away.
i agree putting a break in the dam will work but its illegal in some states and the channel set will work if u put it in then put a stick of a decnt sive over the 330 then they have to go beneath the stick and like he said wham. but your best bet would be to make a castor mound and put a beaver castor lure on it then put a #4 or #5 foot hold trap below it in the water and throw a cinder block out in deeper water wired to a stake on dry land then when it steps on the trap it will catch the foot then it will swim down the wire to the cinder block and quickly expire also the trap is connected to the wire by a universal swivel and i use 11ga wire mostly cause you can buy it at any hardware store and cheeper then from trapping suppliers and for every thing you need send for a catalog or go online to minnasota trap line products and they can get you every thing you'll ever need im not advertising its just what i do