This article is from the Getting A Cat FAQ, posted to rec.pets.cats newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
An animal shelter is a good place to pick up a cat and save it from death in the bargain. Look for a clean, healthy cat. Look for signs of friendliness and liveliness. Talk with the people caring for the animals for any information on a particular animal they can give you; they can often tell you a lot about a cat's personality. Don't overlook the adult cats.
At the animal shelter, be prepared to pay a fee, answer some questions about the home you will give the cat, and perhaps give some references. This is normal. The fee covers some of the costs of operating the animal shelter. The questions are meant to ensure that adopted cats go to good, stable homes.
Most will require that you have the cat neutered. Some will do it prior to adoption, others will require you to do so within a month or two of adoption. THis is also normal and is intended to reduce the population of kittens returning to the shelter. In particular, shelters that neuter all outgoing animals prior to adoption have particularly good success with reducing the overall population of cats in the shelter, since compliance with these programs is 100%. Please neuter your cat if the shelter releases it to you unneutered.