I'm glad you asked this. I ran into this issue when I redid my 1970 Roadster, and because I wasn't entirely sure on the proper way to do it, made a bigger mess than needed.
First off, while your snaps are still on the seat pan, install your new cover like you would if you were snapping it in place. Pull it down snugly over the seat pan with the cushion installed and mark each spot with a gold or silver colored marker (makes it easier to see the mark later). Then remove the cover and install the snaps. You can buy a button snap tool on Amazon or at any craft store for about $15. Just line them up over the holes and press them into place. Because of the nature of the vinyl, getting them exactly right isn't really a problem. Once it stretches a little, no one but you will ever know they might be off 1/8". As long as they're snug, they'll look fine.
If you replace the snaps on the seat pan (and I wouldn't unless absolutely necessary), be sure you buy the right size. I made the mistake of buying a size too large for my seat pan, and ended up having to remove them and start over. To remove the old snaps, I used a dremel with a grinder wheel and ground away the backs of the snaps from under the seat pan. They just fell out. I tried without success to install the new snaps using the standard back. The problem is that the back portion didn't have a long enough neck to reach the inside of the front portion and still have enough lip on it to grab it when mashed down. I ended up using a riveter on them. I put both the front and back of the male portion of the snap onto the seat pan and mashed them down, then put a rivet through the center. This helped make sure they were nice and tight, and wouldn't come off later.
