We went to a pet store today, not to get a cat, but to return an item. I just had to snap a couple of pictures of the adoptable cats making sure the lens of the iPhone was positioned so it could see through the holes in the plexiglass behind which were the cats.
This is probably the easiest way to photograph cats. Another way is to try and get a cat to be interested enough in what you're doing to have them remain in a fixed position long enough for you to snap a picture or three.
Tonight as I tried to get some close up pictures of flowers, one of our cats decided to hang out with me. Since I was already lying down on the ground I just set the camera down and started snapping pictures.
Some shots turned out...
But if you're patient, and the cat is willing, sometimes you can get a great shot. Good luck with all your feline photography endeavors!