Remodeling RV, Need help Finish cabinets
The stuff is called laminate. Formica is a brand name that is commonly used to describe it.
You can usually install it over existing laminate, provided you clean the surface and scuff it up with some fine sandpaper.
You have to have a router and a flush-trim bearing bit to trim the overhang at the edges once you've installed it. It is also easiest to cut with a router.
Formica is installed with contact cement. It is applied with a roller or brush to the substrate as well as the Formica. You let the cement dry until it is barely tacky (20-40 minutes), then slap the new piece over the old. I suggest using wood dowel rods laid flat on the old counter to allow you to position the laminate, because once it touches, you'll never move it again. Starting at one edge or in the middle (working out to avoid high spots), remove the dowels one at a time and press the laminate down. A cheap j-roller or a rolling pin from the wife's kitchen is a must.
Once it is glued down, use the router to trim it. Where the router can't go you'll have to use a utility knife and a file very carefully.