Plant the right plants
Native flora is one of the easiest and most animal-friendly ways to attract all sorts of creatures into your yard, so making sure you're growing plants and flowers like roses to attract caterpillars and birds, gums to attract possums and koalas and fruit trees to attract fruit-eating animals, will mean you have a little wild menagerie of your own!
Food and water
Like anywhere else you'd consider home yourself, animals need their creature comforts like food and water, too, so providing them perhaps a little bird house for shelter or a fountain for running water gives certain species all the more reason to stay, or at very least keep returning.
Keep pets inside
Yes, pets are animals, too, and keeping them inside isn't ideal for all times of day, but if you're after more birds and other creatures hanging around, then perhaps diverting where Fido or Puss spend most of their playtime or bathroom time for a while until other local fauna know where is in and out of bounds.