Your fabric should be the thickness of the eyelet post. First, make a hole in your fabric that allows the female part to fit through snugly. Put the “female” part down on a hard flat surface, on top of that your fabric project with the hole cut out. Now put the “male” part on top and press very hard with the heel of your hand.
I don’t use a hammer. You could do that, but you’d need to cover the eyelets with a dishtowel or other thick fabric. You can purchase a rubber mallet at Home Depot or Lowes. These mallets are usually used to hammer down flooring tiles. Still, I would cover the hardware with a cloth to prevent it from getting scratched.
I find that once they snap together it’s really difficult to get them apart. So they’re pretty secure. If you want a bit of added assurance, you can add a few drops of a craft glue to the inside of the eyelets (GS Hypo Cement works great as does E6000 Craft Adhesive).
Some of the prong applied eyelets that we have work better for thinner project applications.