I have an RV which has a 1-1/2" PVC piping to ventilate the waste tank. I need to extend the roof end of the pipe by about 3 inches or so to install a different vent cap. I have no idea what I'm doing, but my research thus far leads me to believe I should buy a 1-1/2" "slip" coupling and then prime and glue that. Is this a valid approach?
Yes, that will work; coupling, additional length of pipe, adhesive kit, preferably sandpaper to clean the surface before gluing, saw or appropriate-sized tubing cutter if you need to cut the pipe section to length.
I presume you aren't going to have to redo the flashing around the wall or roof pentration; if that has to be disturbed add supplies to deal with that.