Full-grown possums are about the size of a house cat, mostly gray in color, have 50 extraordinarily sharp teeth, prehensile tails, and, to top it all off, opposable thumbs.
Opossum
Opossum 2
Virginia Opossum

Opossums (Didelphis virginiana) just love to climb fences to get into your yard, garden, or chicken coop, tear the lids off of garbage cans and strew trash all about, and destroy your bird feeders as they eat up all that delicious seed. They also enjoy taking up residence in and/or under houses, barns, sheds, dog houses, garages, porches, crawl spaces, attics, and chimneys. And because of their tendency to carry things like tularemia, leptospirosis, murine typhus, roundworm, and equine protozoal myeloencephalitis (EPM), these are not critters you want hanging around. So let's quit wasting time. Read this article, memorize every single word, and learn how to get rid of possum pests.
Possum trapping with a live trap. For this method of opossum removal, which is, incidentally, the best method, it's best to use opossum traps that measure 12" x 8" x 7" and have only one entrance. An opossum trap should be placed near locations where you know the opossum to have been. Generally this will be areas like next to garbage cans, along fences, by chicken coops, near compost piles, and alongside buildings. Secure possum traps firmly to trees, fences, or buildings or stake them to the ground so that possums don't tip them over to get the bait instead of entering the trap.
Opossum bait. The best thing to use as opossum bait is cheap, canned cat food. However, since we know possums will eat almost anything, almost anything will work. In lieu of canned cat food, try using corn on the cob, melon, apple, any other fruit, sunflowers, peanut butter on bread, or sardines. Whatever you use for your opossum baits, place a little in front of the entrance to the trap and a little at the rear of the trap behind the trip mechanism. If the possum you're trying to catch has bait shyness, tie the trap door open for several days and continue to bait. When the possum is taking the bait reliably, untie the trap door and reset the trap properly.
For opossums living under your porch, shed, garage, house, whatever. Start by locating all access points and temporarily block off all but one of them with plywood, tin sheeting, etc. Next, create a one-way door for the final access point. Do this by cutting a piece of ½" hardware cloth so that it's 3 inches larger than the opening on all sides. Hinge the top to the structure above the hole and leave the other sides loose. This will allow the opossum to push the door open to get out but make it hard to get back in. Finally, spread a layer of flour on the ground around the opening. Check for tracks in the morning to see if the possum left and if it got back in.
Block openings permanently. After successful possum removal, it's time to make sure they can't get back under there. To do this, you'll need a below-ground fence. Get a roll of ½" mesh hardware cloth, roll it out where you want it, bend a 6 inch ledge into the bottom of it so that the ledge is coming towards you and away from the structure at a 90° angle, and bury the whole thing 12–18 inches below ground. Once it's buried, fasten the top of the fence securely to the underbelly of the structure it's blocking access to.
Fencing gardens, poultry coops, etc. The technique mentioned above can also be used around gardens, chicken coops, compost bins, etc. There are, however, two main differences. First, the fence will need to be at least four feet tall and the top 12–18 inches should be bent out towards you and away from the garden at a 45° angle. Second, you may need to add a couple electrified wires to keep them from climbing over. Start by running two wires along the bottom. The first one should be 6 inches up from ground level and the second one 4–6 inches above that. Run a third one along the top. All wires should be 3 inches out from the fence. Buy electric fence systems from Havahart.
Opossums in the attic. If possums are plaguing your attic, watch outside for a couple nights to figure out how they're getting in. Once you know where all the entrance points are, wait until dark when the opossums are out and patch those holes. You won't have to get rid of opossums from the attic if they can't get in there in the first place. Trim tree branches that an opossum could climb onto the roof from and get rid of any English ivy. Also, as it's easy for possums to climb the corners of many houses, consider attaching large, slippery squares of metal sheeting to them that possums won't be able to climb past.
Ammonia and mothballs. Ammonia is the most commonly recommended possum repellent. To use it, pour some in an old coffee can or pan and throw an old rag or towel in it to help with wicking the ammonia and dispersing the fumes. Place your chosen ammonia receptacle in whatever little hidey hole you're trying to keep possum-free. While you're placing your ammonia, feel free to toss a few mothballs around.
Take care of your trash. Get cans with tight-fitting lids, strap down the lids of the cans you already have, or put rocks/blocks on top of them. Put cans in a trash can rack so they can't get knocked over.
Quit feeding pets outside. Opossums adore dog and cat food. They can't get enough and view pet dishes as an open invitation to your yard.
Don't feed the birds. Possums love black oil sunflower, striped sunflower, peanuts, and suet. If you want to get rid of possums more than you want to feed the birds, take those feeders down.
Get a new compost system. Possums enjoy snacking on fresh compost. Carrots, potatoes, fruit, all of it. It's delicious. Get an enclosed compost bin that possums can't get into.
Pick up fallen fruit. Instead of luring opossums in by allowing fallen pieces of fruit from trees to sit on the ground to rot, rake 'em up, pick 'em up, and put 'em in that new compost bin.
Destroy potential den sites. Getting rid of possums is easier if you destroy the spaces that provide for good places to live. Remove hollow stumps and fill rock crevices, old burrows, and other openings.
Remove hiding places. Remove brush piles, mow your lawn and cut back any tall weeds and shrubs. Rake and get rid of old leaves and fallen weeds. Possums use these items for lining their dens.
Opossums tearing up your lawn? There's a damn good chance you have a large grub contol problem under the sod.

Predator urine. If an opossum thinks there's a fox, coyote, wolf, or bobcat around, it seems unlikely that it'll want to stick around the vicinity and become something's dessert. Look for possum pest control products like Shake-Away that utilize predator urine as an opossum repellent.

Crushed garlic. While most people find the smell delightful, opossums apparently do not. Place a whole bulb or two of crushed garlic in a bowl and set the bowl down in the area you are trying to keep opossums out of.

The Scarecrow. This sprinkler is one of my favorite products of all time. It's motion-activated and designed to squirt at and scare the piss out of passing critters with jets of water. Along with the jets, the sound of it kicking on also helps to startle opossums into hightailing.

Lights and radio. Placing floodlights in areas where opossums tend to convene is a good way to keep them away. Place lights at the opposite end of the entrance so that they shine possums in the eyes when they enter. Possums are nocturnal, so light = bad. For added protection, set up a cheap radio down by the lights and set it on a talk station.