Groundhogs, as a species, have a large range in size. There are the medium-sized rodents I grew up with, averaging around 4 kg, and groundhogs—like a certain Phil—that are probably more like 14 kg. This is the likely source of my earlier confusion, as that's a huge discrepancy in size. Evidently, it's all in the diet, much like humans.
Where I grew up, in rural Northern Minnesota, we called the groundhog a woodchuck; I thought that the groundhog was some fat cat, East Coast, liberal rodent. As it would turn out, they are actually one in the same creature—Marmota monax, a member of the squirrel family. Woodchucks spend a lot of their time in burrows. It is their safe haven from their many predators, and they are quick to flee to it at the first sign of danger. They will sometimes emit a loud whistle on their way to alert others in the area that something is awry. Groundhogs enjoy raiding our gardens and digging up sod, thereby destroying what we've spent countless hours toiling upon.
Look for groundhog signs. You might not even know there is a groundhog around until your garden has been devoured or your tractor damaged by a collapsed groundhog den. Things to look for are large nibble marks on your prized veggies, gnaw marks on the bark of young fruit trees, root vegetables pulled up (or their tops trimmed off), groundhog-sized holes (25–30 cm) anywhere near your garden, or mounds of dirt near said holes. If you see these signs, take action. Don't wait or it will be too late! If you know it will be a problem and do nothing, you can't blame the animal.
Set groundhog traps. This technique takes some skill as you need to be able to pick a spot in the path of the animal, camouflage it, and mask your strong human scent. Setting a spring trap, whether coil or long-spring, is usually just a matter of compressing the springs and setting a pin that keeps the jaws open into the pan or trigger. Make sure your trap is anchored securely with a stake. Check your traps often, and dispatch the animal quickly and humanely. Shooting them in the head or a hearty whack to the head with club will do the trick. If you can't deal with this, you have no business setting traps. Call a professional.
Guns kill groundhogs. I have never shot a groundhog. I rarely have had problems with them, and they move so damned fast it is difficult to get a shot off. If I had to, I know how I would do it. First, be sure it is legal in your area, and be sure to follow gun safety protocols. After that, it's just a matter of learning where your target is going to be comfortable and let their guard down. I would follow their tracks back to their den, find a spot downwind to sit with a clear shooting lane, and make sure nothing you shouldn't hit with a bullet is down range. Then, I would wait, my sights set on the den, until the groundhog stuck its head up—quick and easy.
Demolish the groundhog burrows. If you find a couple holes around your yard, they are likely the entrances to an elaborate tunnel maze carved into the earth beneath you. About all you can do, short of digging the whole mess up, is to try and fill it in from the top side. First, fill it with a bunch of rocks and then soil—make sure to really pack it in. This will make it difficult for the groundhog to reclaim its hole without a lot of work. You probably want to do this in tandem with other control methods such as trapping, shooting, or fumigating to prevent the groundhog from just digging a new hole.
Do some landscaping and build barriers. As with the control of many pests, it is advisable to keep a yard free of brush, undercover, and dead trees. These types of features are attractive to groundhogs as cover, and without it, they are less likely to want to spend time there. If you want to keep a groundhog out of an area, consider a partially buried fence. This will require a lot of work, but it is going to help a lot. Make sure it extends up at least a meter, and that it is buried somewhere around 30 cm deep. Angle the fencing outward 90 degrees when you bury it, and it will make digging under it a very daunting task for your furry friend.
Try using fumigants to kill groundhogs. What is nice about this product is that you can kill the animal and bury it all in one stroke. The best time to do this is in the spring when the mother will be in the den with her still helpless young. Also, the soil will likely be damp, which helps a lot. You should definitely follow the directions on the package, but the way they usually work is that you cover all but one exit, set off the smoke bomb, shove it down the hole, and quickly cover it up. Check back in a day or two to see if there is any sign of activity, and if so, do it again or consider a different control method. It is important that you don't do this if the hole is next to your house or if there is any risk of a fire.
Poisons are a last resort. I am not a fan of poisons because it is difficult to target what will eat said poison in the wild. Also, you are left with the issue of where the groundhog will die and how bad it will smell if it is somewhere under your house. Or, if it is outside somewhere, who will be affected by eating the dead animal? Where does it end? If you want to use poison, you're on your own.
Use live traps. This is a good option for those of you not too keen on killing things. Try jamming the door open and leaving bait inside for the taking a couple of times so they get used to it. Then, set it normally and you've got your groundhog (or a neighborhood cat). Now what? The relocation is just as important; you need to choose a place that is far away from other humans and can likely support a groundhog. Good luck.
Predator urine. The idea is simple: form a perimeter around an area you want to protect. If the groundhog doesn't recognize the smell as a natural predator, it is probably not going to work too well. Look for brands that have wolf and bobcat urine. Apply regularly, or as the manufacturer recommends. Remember, if it rains, the urine has probably washed away.
Repellents. Another popular method involves pepper-based repellents. These deter groundhogs by tasting horrible and burning their mucous membranes. You can do a perimeter with powdered cayenne pepper or just apply it to the things you want spared in your garden. Be sure to wash your vegetables off before using them (which you should be doing anyway).