Lay a thin straightedge on top of the fridge and run a pencil across its length. Repeat along the side of the refrigerator where cabinetry is not present, whether one side or both. These marks outline the refrigerator exactly.
Pull the refrigerator out. Unplug it if absolutely necessary to allow you to move it far enough away to clear your work area. Use another plug receptacle if possible.
Consult the manufacturer's specifications to find the clearance necessary around your fridge, both side-to-side and above. Clearance minimums are at least 1/2 inch. Measure from the previous fridge outline markings over the amount of clearance area required. Repeat measurements in a couple spots to ensure accuracy. Use a level as a straightedge to mark the clearance guide, checking for level or plumb before proceeding.
Tap on the wall behind the refrigerator to find the studs -- the vertical wood framing members -- in the wall. Mark an X along the clearance guideline where a stud is present. It should feel solid and emit a thud where there's a stud, but it should feel soft and sound hollow when there isn't. Find the joists in the ceiling directly above the walls and fridge similarly. Whenever possible, walls should anchor to adjacent walls and ceiling joists.
Measure out from the wall, aligned with the vertical wall placement lines, to the length of the wall required. Mark the wall placement and length with a straightedge and pencil or tape. Repeat for any additional walls.
Cut two 2-by-4-inch boards to the length of the side wall involved. These will form the top and bottom plates for the wall beside the refrigerator. If two walls are needed, cut four plates total. Use 1-by-2-inch boards if you prefer a thinner wall.
Measure the floor-to-ceiling height to determine the length of studs needed. Subtract the thickness of both plates, combined, plus an additional 1/2 inch for clearance when erecting the wall. Thus, if the distance between floor and ceiling is 96 inches, take away 3½ inches for 2-by-4-inch framing. For 1-by-2-inch framing, deduct 2 inches.
Mark each plate to indicate the beginning stud and the middle of each successive stud, including the last. Lay a framing square across both plates at once and draw a line across the edge to make the stud marks. Space studs equidistant across the plates, making the center of each 16 inches at most, or closer for greater strength.
Construct each stud wall, nailing through the widest face of the plate into the end of a stud with two 16d nails. Turn the studs so the widest face also runs vertically. Align each stud flush with the plate end or with a stud mark. Attach the opposite plate to the free ends of the studs.
Erect each stud wall built. Align the wall with the guide marks. Use a level to ensure the wall is plumb -- straight up and down -- before securing in place. Make the wall fit snugly by shoving thin wood shims under the wall. Nail through the bottom plate into the floor beneath. Attach similarly along the ceiling. Drive additional nails through the first stud into the wall framing behind the fridge. Test to make sure the wall is sturdy before proceeding.
Cut four additional boards, using the same dimension board as previously used, to fit between the walls on either side of the fridge. Insert them, two in the back and two in the front of the space between the walls, to create a box outline. Nail them in place to secure them. These create the frame for the soffit above the fridge.
Finish each wall as desired. Quarter-inch veneer works well to line the walls and underneath the soffit, from inside the fridge enclosure. Use the same material for the exterior face of the soffit and exterior wall surface as well, or any combination of drywall and wood. Paint, stain or apply drywall tape and compound as appropriate. Slide the refrigerator back in place when the job is complete.