Familiars are kind of confusing, it depends what you believe really. Historically it was believed a witch would get their pet to do their evil bidding [or they could also transform into them, can't remember exactly] so if something bad happened and someone noticed a cat, it was the evil doings of the creepy old lady who owns said cat.
Today I've heard a few claims what familiars are, some say it's an energy form you create, others it's an actual animal you put energy into, or an animal you have a spiritual bond with. Personally, it's an animal with a spiritual bond. You can also train your pet to help/join you in your craft, but not all animals will be true familiars. Familiars can sense energy, so while you may be able to train your dog to sit in a certain spot in the circle, a cat would be harder. An author I love writes how her one cat could sense the energy, and would walk around the circle, but her other cats could not, so all but the one cat needed to be put in a seperate room.
Meanwhile, if you wish to train your pet, there are many ways to try, but it takes time and you need to figure out the subtle cues of the animal, you can train it. You can train your pet to rest beside you or in your lap while meditating, but regard the animal, if it seems like it wants to play, don't force it to sit still.
The meditation seems interesting, might try it if I get a pet one day.