Survey the home and determine where a central wall location is that is easily accessible from all areas of the home, and especially from where you spend most of your waking time. The wall needs to have an open area where a picture would look reasonably placed.
Find the wall studs and measure the space between them. It should be 16 to 18 inches wide.
Saw a hole between the studs carefully with a rotary blade or drywall saw. The insides of the studs should be exposed on either edge.
The hole should be high enough to comfortably hold your handgun with room enough to reach into it.
At the bottom of the hole attach a 1-by-2 board lengthways across the opening with l-shaped brackets and small wood screws. This prevents the firearm from falling down behind the drywall by accident.
Fasten a pegboard between the studs in the open area and toward the back of the opening. Attach pegs of sufficient length to the pegboard to hold the handgun in place.
This may take several attempts at locating the pegs before you find the most comfortable way to reach in and obtain the handgun.
Apply drywall tape and mud to the exposed edges to prevent dust from leaking down onto the floor.
Hang a suitable picture over the exposed hole to prevent anyone from seeing the opening. Ensure the frame is heavy enough so that a simple nudge will not move it, but light enough to purposefully move one-handed and in a hurry.