Underneath you'll find to water connections, hot and cold water. They screw onto the faucet inlets. The single handle is simply a ball-type mixing valve that shuts off all water flow.
Is this what yours looks like?
If that's looks like yours, I recommend removing the faucet, going to your local Lowes, Menards, etc hardware store and buying a household faucet that matches the mounting holes/water inlet nipples, and installing it. The RV type are normally chrome-plated plastic like the one in that hot link. Probably cost nearly as much to repair your present one than buy a new household type that is all metal.
The water hoses normally have threaded connections to the faucet, and are hand-tightened.
2000 Winnebago Ultimate Freedom USQ40JD
, ISC 8.3 Cummins 350, Spartan MM Chassis. USA 1SG, retired;PPA,Good Sam Life member."We the people are the rightful masters of both the Congress and the Courts - not to overthrow the Constitution but to overthrow men who pervert theConstitution. "Abraham Lincoln"