Trace the back of the medicine cabinet, along the wall, with your pencil. Now open it and look inside for its mounting screws. If the cabinet's screw holes have a keyhole shape, you can slide it up and off its mounting screws when you loosen them with your cordless drill. If not, unscrew them from the wall and set the cabinet on the floor.
Notice where the cabinet's screw holes appear within your pencil border. This is the location of the vertical studs behind the drywall. Rap the wall with a knuckle between these screw holes to find out where the hollow space ends and the inside edge of each stud begins. Mark these points with your pencil. Studs are generally spaced 16 inches on center from each other.
Use your level and pencil to draw a square several inches within the pencil border you traced in Step 1. This square should line up with the marks you made in Step 2. Center the air bubble on the level before drawing your vertical and horizontal lines, to make sure they are straight. Now use your drywall saw to cut out the square you just traced and remove it from the wall.
Measure the distance between the studs, where your hole is, and put a mark on the front and back edge of your 2-by-4 at this length. Use your level to draw a straight line between the marks and cut along it with your saw. The 2-by-4 should be just long enough to have a snug horizontal fit between the studs.
Place the 2-by-4 shelf you just cut at the bottom of the square hole in the wall and push it into a horizontal position between the studs. Lay your torpedo level on top of it and adjust the ends of the shelf until the bubble on the level is centered.
With your cordless drill, screw the 2-by-4 shelf to the studs. Use two screws on the left side, two more on the right and drive them through the shelf and into the studs at a 45-degree angle. Place your valuables on the shelf and remount the medicine cabinet to cover your hole.