The first step in faucet bib insulation is to winterize your faucets properly before freezing temperatures arrive. Disconnect all hoses. If you have shutoff valves on the inside of your house for the faucet bibs, turn them off and drain the remaining water from the bib.
Faucet bib covers are the easiest way to insulate your bibs. They're dome-shaped and made of Styrofoam. They usually come in white, gray or green. If you're concerned about matching your house, you can spray paint them a complementary color. If you have shingled or uneven siding (such as brick) that won't let the cover sit firmly against the side of your house, glue foam rubber to the cover's edge. The foam rubber will compress and form to the side of your house. Be sure to use a thick enough piece of foam rubber to accommodate your siding.
You can use other products if faucet bib covers are not an option. For example, a spray foam product will seal around the faucet bib, holding heat in. There are also insulated bags called faucet socks that fit over your faucet bib.
Consider installing frost-free faucet bibs. They operate in the same way as a shutoff valve installed in your plumbing. Frost-free faucet bibs have a stem that extends into the house, where the water is cut off from the outside wall of the house. These kinds of faucets are now a part of many building codes across the country. They are also called anti-siphon freezeless yard hydrants.