hanging long shelves on a mobile home wall
Mobile homes have vertical studs just like a wood frame house. These may be 2x3" x ~8 ft rather than 2x4" as in a fixed structure, but they will still support a shelf if done properly for the expected load on the shelf. The studs will be 16" apart or 24" apart.

You must locate the studs and attach the fasteners through the finished wall (paneling or drywall) into the studs. Also be sure you do not drill into an electrical wire in making holes for the fasteners.

An electronic stud finder is useful to locate the studs, but it does take practice to learn how to use these correctly. Some people use magnets to find the studs by finding the nails used to attach the interior finish wall panels to the studs. Some people can locate the studs by rapping on the wall with their knuckles.

Addition

Electrical boxes for receptacles or wall switches in houses are usually attached to the sides of studs so if you have a receptacle under where the shelf is to be, then there would be a stud on one side or the other of the receptacle. But in at least some mobile homes the receptacles are not attached to studs.  In any case once you find a stud by some means you would look for other studs 16" (center-to-center) away on both sides, but the distance between studs is not always 16" and some framing is 24" on centers.