Place the wooden desk extension panel on the floor. Decide which end will attach to the original desk. Make three small marks along this side, spaced evenly apart. The marks must be in the middle of the height, meaning the mark is placed 1/2 inch down on a 1-inch-thick desk surface.
Drill 1/2-inch holes in the side of the desk where the marks are using the 1/2-inch-wide bit. Apply wood glue in the drilled holes. Insert wooden dowels in each of the drilled holes. Hold them firmly in place for a minute to ensure they connect.
Hold the extension panel with the dowels up to the side of the original desk that faces the desk extension; consider using a level set across both surfaces to be sure they will be even when the extension is attached. Use the pencil to indicate where the three wood dowels on the extension desk hit the original desk's side. Drill three holes on the original desk in the same manner as on the extension.
Attach the two desk legs on the extension at the end opposite the dowel joints. Use installation screws and a hand-held screwdriver. The set of legs on the original desk next to the extension will provide support in the middle of the desk; the new set of legs will support the end of the new part.
Apply wood glue in the holes on the original desk and along the side. Hold the desk extension up to the original desk and slide the wooden dowels sticking out of the extension piece into the holes on the original desk. Hold the two desks together using an extra pair of hands or the wall for support. Wipe off any excess glue with a cloth.