How do I install an outdoor receptacle box on vinyl siding?
You can probably get away with a weather proof box on top of the siding, but here's the full procedure to make it look nice.

Vinyl siding can be pulled off and later reattached. To remove it, you need a siding removal tool that has a flat blade with a small hook on the end. You shove it up the gap between two pieces of siding and then pull to separate them. Start with the top edge that you want to remove, expose the entire piece, and then unscrew it from the wall.

There should be tyvek or similar weather proofing material under the siding. Repair the screw holes and any tears with tyvek tape.

Locate your new outlet installation location. More than likely, you'll need to remove the drywall inside to feed the lines to this outlet, so find your stud there and drill a small test hole. Make sure the hole is near where you want to place the electrical box, cut back the tyvek in an X shape with the, and then cut your opening with a drill in the corners and a reciprocating saw.

Install the new junction box to the stud. You may find it easier to screw it in since hammering requires space to swing the hammer and the vibration could cause damage to the surrounding drywall. Caulk all gaps around the box and the outside sheathing. Cut back any excess tyvek and tape around all 4 sides to make it weather tight.

Run your wiring. Don't forget to staple it to the center of the stud. Install your outlet, making sure it's GFCI protected since your outside. Use a weather protective cover over the outlet.

Install J-channel around the outlet. Install from the bottom up and overlap the joints so any drips go outside of the J-channel. Begin reinstalling your siding from the bottom piece working your way up. Measure twice around the outlet and cut your siding with tin snips (it will go through like butter and leaves the best edge for small cuts). Remember to measure so the cut is inside of the J-channel and you have a 1/4" of play to each side (siding moves with temperature changes). Don't forget to account for the overlap with the adjacent pieces when measuring, and when reinstalling, the overlap should be such that you aren't looking into a gap from the predominant view of your home. When reinstalling the siding, give it a good shove against the track on the piece below until you hear or feel it click in all the way across.

When screwing back in, I'd use different screw holes and new screws. The screws should have a flange so the siding can't slip over the head, wide threads to bite the wood, and be relatively shallow so you aren't going completely through your sheathing (1/2", maybe 5/8"). When screwing in, put your screw in the middle of the slot at the top of the siding so the siding can move from side to side. And leave the gap of a fingernail under the screw head, don't tighten it all the way down. For the last piece, after you've screwed it in, pull down the siding above into the track, and snap it in with a firm shove. The siding removal tool can help you line this up.