Some TTs with sandwich type exterior walls and aluminum framing will only have studs in the corners (already noted above). The TT in your profile looks to have aluminum siding in which case it will have wood framing. To find studs, you can look for a vertical line of teeny tiny staples and a stud will be behind them. At joints in the luan plywood there will be tape over the seam with the same wall color. You can push a thumb against the laun horizontally and see where it doesn't flex. There's no standard stud spacing so don't assume they'll be every 16". You could try lightly tapping luan with a hammer until you find where it seems solid. You may or may not find that a stud finder will work. Sometimes you can look at the exterior walls early in the morning and see dew where the studs are. Another thing that might work is a IR gun used early in the am when it's been cool overnight and when the TT has been heated for some period of time.
Mounting/attaching things to a wall depends on it's size and weight. RV manufacturers typically use #8 screws into the luan plywood only for just about everything (cabinetry, dinette seating, etc). For something heavy or subject to being pulled off (towel bar, eg.), Oscar rivets work great. They're a special type of pop rivet designed specifically for RVs. Otherwise smaller #6 screws may work or Command strips.
Screwing into studs would be the strongest but make sure screws are the right length so they won't go through the siding. For heavy items like say a TV, you will have larger dia. screws and will want to screw into the dead center of the studs (they're not very wide) and may need to drill a pilot hole first.