Some kitchens are designed with counters that do not run all the way to the wall. Whether this is part of a purposeful design, allowing for access to a garbage can or other items, or because the original designer gave little thought to how counter space is used, you may want to fill in the gap between your kitchen counter and wall. Doing this takes some concentration, and you'll need to have several hours free to get the job done right. It is not a complex undertaking, but requires you to be specific in your measurements and construction.
Locate the studs in the wall where you will be attaching support pieces for the counter extension. Turn on the stud finder, and drag it slowly (below the level of the existing counter) until it indicates the presence of a stud. Mark the wall with a pencil at that spot.
Measure the gap. Hold the end of your tape measure flat against the wall facing the counter, and measure to the beginning edge of the counter top. Then, measure from the back wall to the front of the counter.
Make the support pieces by cutting four furring strips from the 2-by-1 wood. Cut two to match the width of the gap (from counter to facing wall) and two to match the depth (from back wall to front of counter). Subtract 2 inches from the width measurement, before cutting the two depth pieces. You will be placing the depth pieces perpendicular to the width pieces and between them, so the depth pieces must be 2 inches shorter.
Use a level to draw a line on both walls at the surface height of your existing counter.
Measure down from that line the exact thickness of the particle board and Formica that will become your countertop extension. For example, if you have a 1/2-inch-thick piece of particle board and will top it with a 1/8-inch-thick piece of Formica, measure down 5/8 inch from the line. Use your level to draw a new line at the height of these marks.
Screw the support pieces into the studs you had found. Install the back width first (that runs along the wall), then the two side pieces (one attached to the wall and one to the existing counter), and then attach the front width piece to the two side pieces.
If you are using the exact same countertop thickness as the existing counter, you will not be able to screw the side piece into the side of the counter. Turn the piece on its flat (the wide face) and screw it to the underside of the edge of the counter (the lip) so that half of the support piece is under the counter and half is sticking out into the gap.
Attach two small, flat metal mending plates between the support pieces and the underside of the existing counter. Do this so they cover the two joints formed where the back and front width supports meet the counter.
Measure and cut your particle to fit the gap and rest on the support pieces. Keep the particle board flush to the face of the front support piece, not extending over it.
Trace the shape of your particle board onto the backside of your Formica. Use a box knife to cut the shape out of the Formica. Do not try to cut through the Formica with one try; instead, score the surface and then keep cutting along the mark, applying gentle pressure until you break through.
Lay the particle board into the gap so it rests on the support pieces. Screw the particle board down into the support pieces.
Apply epoxy to the particle board and to the backside of your Formica. Wait until the epoxy becomes tacky (sticky) to the touch, and then press the Formica into place.
Cut a piece of Formica the length and width of the front support piece, and epoxy it into place. Allow the epoxy to fully cure, at least 12 hours, before using your countertop extension.
Placing your marks below the level of the existing counter will ensure that they will not be visible when you are done with this job. No matter what material you choose to cover your countertop extension with, the key to making it look good is to match the height of the front edging piece to that of the rest of the counter. This way the extension will not look "out of place" but like a deliberate design element.
Be aware of what you are attaching the extension to, and use your extension accordingly. If your extension supports are screwed into drywall only, do not overload the extension with heavy appliances. Doing so may cause the supports to tear out of the drywall and the extension (and everything on it) to fall to the ground, potentially damaging your appliances.