Measure and cut 2-by-4s with a circular saw to the height you wish the sink stand to sit. Cut two boards per corner of the stand, and then attach pairs of 2-by-4s together by driving deck screws through the pairs of boards.
Cut more 2-by-4-inch boards to the width and depth you plan to make the sink cabinet, making the cabinet larger than the sink you plan to install. Overlap the new boards over the pairs of boards, and then drive deck screws through the connection holding the boards together.
Measure the sink cabinet’s frame’s top and sides. Cut plywood that fits over the cabinet’s sides and top, leaving an open area directly below the sink so you can access its plumbing later. Attach the plywood to the wood frame by driving deck screws through the plywood and into the wood frame.
Measure the cabinet base’s opening where you access to the sink’s plumbing. Cut a separate piece of plywood that fits in the opening. Attach hinges to the plywood door’s top and bottom and the adjacent plywood using screws.
Flip the sink upside down and place it on the top of the stand. Trace around the sink’s perimeter and then remove the sink. Using a ruler, draw a second line one-half inch inside the line you traced.
Drill into the edge of the smaller tracing you drew and insert a jigsaw’s blade into the hole. Cut along the smaller tracing you made. Apply a bead of silicone caulk around the sink cutout and the place the sink in the cutout. Use a rag to wipe away any caulk that spreads out from under the sink’s lip.