The word familiar comes from the latin word "famulus" or attendant. A familiar is much more than a pet, and not all pets become familiars. Basically they are magickal helpers whom you have a spiritual connection with. They can at times warn you of danger, give you protection and defend you. They also have healing powers and quite often are a calming influence.
They are here on Earth to teach you and if you are interested in familiars, totem animals and spirit guides, then it is recommended you research this area further and look into Shamanism, Totem Animals and Native American Indian teachings.
Black cats are probably most identified as the witch's familiar but that's not always the case. Many different kinds of animals can come to you as a familiar and I am sure you will know when they do, and trust me you will know. Your familiar could be anything from an owl, a dog, rabbit, ferret, snake, blackbird, or a spider, the list goes on.
It is not necessary for you to have a familiar or work with one as a witch/pagan/wiccan, rather that they are available to work with if you are open to the idea and of course you need to feel comfortable doing so. Sometimes just meditating on a chosen totem animal/spirit is enough for some, I myself use Druid Animal Cards and meditate on specific animal energies at times. Some witches/pagans/wiccans prefer to work with spirit guides. There is no one right way except the way you feel comfortable with on your path.