I'm not sure if "installing" is the right word, but here goes. Different snaps may require different tools (for example, I haven't figured out how to put in a pearl snap without cracking it), and you can even buy snap tape... but I put in snaps the ol' fashioned way. I have tried that plier/hole punch looking tool but I couldn't get the snap to align properly. I bought the package of snaps at Wal Mart that comes with the tool, and now I buy snaps in bulk but I still use the same tool. I put snaps in my Irish flat caps, so that is what you will see in the examples.
So one snap requires four pieces, the front and back and a prong for each. For lack of sounding like a 7-year-old-boy, I will refer to the front and back as "male" and "female" parts, isn't that pretty standard hardware store speak?
Here is a nice close up of the female piece. Let's do this one first since it's trickier (snaps are a bitch, ahahahaha sorry 'bout that one). Notice that the inner ring extends on one side. That will be important later on. Oh, yeah, see that steel block in the background? I bought that for jewelry metal-stamping for super cheap with a Hobby Lobby coupon, and I use it for snaps as well. You want a nice hard surface for doing snaps.
Start by putting the pronged piece through the back of the fabric, assuming you have marked exactly where you want the snap placed. The prongs should be poking through on the right side of the fabric. If your fabric is thick you may need to use your fingers or an eraser to help push the fabric down exposing the prongs.
Now place your female piece over the prongs WITH THE EXTENDED SIDE DOWN. Let me say it again, the part that extends on one side should be face down on the prongs.
Make sure the pieces are aligned and place the tool over the snap.
...and hammer hammer hammer! (That's what we say to my youngest when he's playing with his toy hammer). Just a few good hard taps is fine.
And now repeat the steps to put in the male piece.
Prongs through the back end...
Snap goes on top (it can only go one way)... hammer hammer hammer!