When you find an animal that may be a good fit, introduce him or her to your entire family, and to your other pets if the rescue group will allow it. It's important to watch the animal's disposition, especially around children. Most organizations ask you to fill out an application. Some ask you to sign a contract ensuring the animal will be taken care of - or returned to the group if necessary. Each group has its own requirements.
Most rescue groups are nonprofit.
Find out as much as you can about your pet and its needs. There are countless books on all types of animals. You can also find valuable information online or by calling shelters or rescue groups. Then by all means, don't. You can still help area rescue groups by donating money, blankets, toys and other things.