Opossums are known to cause quite the annoyance to homeowners by getting into the garbage, dog or cat food, the duck pen or go even as far as setting up residence in your basement or attic. The most common misconception is that they are dangerous, while their defensive mechanisms could cause some minor damage and pain; they are not as harmful as movies would portray them.
Okay, you have decided to take action if you have come this far. So the first thing you should do is eliminate the source of food. Possums don't randomly go to places, they look for food, even thought they could eat almost anything you could think of. Hence the garbage digging, clean up the area and prevent them from getting into your garbing by using tight fitting cans. If you have a garden, you should set a proper fence around it if you have fruitful trees, and then get your kids to pick up the fallen fruit. Just joking, your kids have better things to do, you should do it yourself. I could go on and list a hundred other things, but you got the point, figure out how to proceed according to your particular situation.
The next step is to locate its shelter if it has one. If you have a woodpile, then that's a good place to start looking. Any kind of tight space could be a good shelter for possums as well as any kind of area which is shut such us the attic or the basement.
Opossums have a well-developed nose, which in a way is a blessing, but you could use it as an advantage. Just bombard them with something which smells heavily like ammonia. Do that in every place you presume the possum might be hiding and shut out any other potential shelters. The smell will for the possum out, and you don't want it to relocate from your trash bin to your basement, do you?
In no case do I mean that you should kill it. It might be quite ugly and cause you extreme amounts of nuisances, but that apart the creature is harmless. What you should do is go to your local hardware store and pick up an adequate opossum trap. Once you pick it up, set the bait. Bait could be any smelly food, such as old vegetables and fruits as well as canned dog's or cat's food. Once you catch him, just drive out with the trap a few miles away to the house of your lifelong enemy. Again joking, find a spot which is not too close to other residential, open the cage from a good range with some kind of a stick or other object, otherwise the possum might bite you and let the create out into the wild.