About this time of year, at least around here, the females distribute their young to old burrows, and then visit them for awhile. The young hang around for about a month and then go elsewhere. If you've got a young one it might move on it's own. I don't think filling burrows works--ground hogs can dig really fast. I read they are known to excavate 700 lbs. of soil for a burrow.
We've got one on the edge of our bush right now. Comes into the yard to mow the red clover and several other broad leaf plants. We're just going to leave it alone unless we get a burrow under one of the buildings, then it'll be time to borrow the neighbou'rs .222. However, understandably you can't tolerate ground hog burrows in a horse pasture.
Shooting is perhaps the most humane method, if that's a consideration. I think one of my cousins used to use leg hold traps-- I wouldn't.