The ways they achieve this goal are varied - from having a leopard's spots tattooed all over their bodies, to shaving off their eyebrows, to bisecting their tongues, to various methods of scarring (burning, cutting, etc.) to having noses reshaped and eyes lifted to appear more catlike.
I remember seeing something like this on an episode of Nip/Tuck, and of course, I've seen many photos of Jocelyn Wildenstein (recently featured here in my blog), who it appears was going for the "lady cat" look...but I guess I really still thought this sort of thing was mostly science-fiction. I guess I also thought that a person would be hard-pressed to find a surgeon willing to indulge this particular type of request. I stand corrected.
Oh, and by the way, if your leopard spot (or tiger stripe, or lizard scale) tattoos start to seem like a mistake a few years (or hours) down the road, check out this article on laser tattoo removal and this laser tattoo removal photo gallery.