This may help you understand a bit. :)
As previously said, familiars can be of the physical plane, but also of the astral plane. I personally have, well, had two familiars. I still do have one, but the other said had passed on. Her name was Isabelle and she was a scarlet dragon. I only communicated with her twice, the first was a skeptical meeting. She didn't trust me, and I was afraid of her. We hardly spoke. But the second time, I recall crying as I sat in my garden, petting her head as she lay dying in the astral plane. Before she had passed on, she left me her egg and told me to take care of the baby. That takes true friendship and love to do something like that. In short, she chose me and I'm glad she did.
In time, your familiar will come to you, whether astral or physical. I was lucky to have both. And I still have one! My cat name Levi. I adopted him from my cousin because she was having her baby at the time and couldn't afford having him jumping into the crib. All her animals were afraid of me, for whatever reason, but Levi came right up to me and wouldn't leave me alone until I left. Within the week, he was mine. Years passed, and our bond grew, and now he's best friend and I would be terrified if something were to happen to him. Just last week, I was talking about familiars with a friend on Skype and Levi cocked his head as if he understood. I simply acknowledged the look, asked if he would like to my familiar, and he 'smiled' at me, crawled onto my lap, and licked my hand. I took it as a yes.
There's a variety of ways to find a familiar. They can choose you, or if your bond is strong enough with one of your pets, you can simply ask them if they would like to take on the duty. If they do something that seems like a 'No' to you, it's not quite the time. But I'm confident you will find yours if they don't you first. :)