Naturally they would use holes in trees, crannies in rocks and secure places in trees and hedges to build their own. Offering a wide range of natural habitat in your garden will present birds with many handy spots to build their own nests.
Different birds have different nesting habits. Wrens like to build a cave-like nest of moss low down. Blackbirds will make a mud and twig open nest higher up in hedges. Finches make elegant pockets in trees.
With habitat at a premium, many birds will readily take to artificial nest boxes. There are many styles and designs made for different sorts of birds and their preferred nesting habit.