The conventional method would be to use a weasel box (a box made of old wood about 6"x6"x12"). It should have a removable top and a 2" hole in one end. A rat trap or a #1 claw trap is placed just a couple inches inside the hole to catch the weasel. Some kind of bait, such as raw meat is placed at the back of the box to lure the weasel in. (They are attracted to the smell of blood, according to the theory).
Unfortunately, the conventional method has not worked for me yet. The weasel's kill is close by and he comes back every few hours to eat a little more; so I guess the box isn't very enticing to him. (I don't want to remove his kill because he might decide to get some more of my animals when this one is gone.) I tried placing glue traps around the kill (you know, the one's that they sell to catch mice and rats), and I've got a couple of nice weasel footprints in them. But the weasel just didn't stick. Right now I'm trying strips of duct tape placed sticky-side-up around the kill. Duct tape should be harder to shake off than those glue traps. We'll see what happens. I hope these ramblings help! Good luck catching your weasel!