Despite their reputation as being pests, possums (or opossums) are in fact useful little animals in your garden. They eat real pests such as slugs and small rodents and rarely cause problems themselves. Possums are also entertaining to watch because of their agility and intelligence. As with other wildlife, much of the natural habitat of possums has been lost to development and agriculture. This means you can encourage them to visit your yard by providing food and places to nest.
Provide a possum feeding station, which can be as simple as a couple of bowls on the ground. Omnivorous possums appreciate meaty treats such as cat kibble as well as fruits and vegetables. Don't put out human food, especially junk food. Possums may well love such food, but it is not good for them. Ideally, put the food out in the evening, watch the possums feeding, then remove the food bowls so you don't wind up feeding rodents.
Encourage other wildlife to provide possum prey by gardening organically and planting a dense variety of plants. Possums need to obtain most of their food from natural sources.
Keep pets inside at night and supervise them outside during the day. Cats and possums are rarely a threat to each other, but a large cat may attack possums and could discourage them from visiting. A dog is a threat and may kill possums if unsupervised.
Install a possum nest box to mimic the tree holes that possums use for nesting. A possum nest box is essentially like a large bird box with a 5-inch diameter hole near the top. The Australian government provides detailed instructions for making possum boxes, which are the right size for North American opossums as well. Attach the nest box 6 to 10 feet up in a tree.
Provide an underground burrow or den. Some possums prefer to nest in the abandoned burrows of other animals, so make an artificial one. Dig a trench about a foot deep and a foot across, then cover with sheets of scrap wood. Leave an entrance gap of a few inches. Cover the wood with anything you like, such as plants, a small shed or a pile of scrap wood and branches to provide a refuge from other wildlife.