Position the sink face-down on the countertop, making sure the space at the front and back is even. Draw a pencil guide line around the sink (Image 1).
Measure the depth of the lip of the sink, then mark a second pencil line at this distance inside the first, all the way around (Image 2).
Use a drill with a flat bit or auger bit to make a hole in each corner of the sink position, inside the inner guide line. Make sure that the drill is at precise right angles to the countertop, so that you make an accurate hole (Image 3).
Cut around the inside guide line with a jigsaw, using the holes as starting points (Image 4). Support the countertop underneath as you cut.
Check that the sink fits well in the hole. Seal the cut edges of the countertop with a preservative primer (Image 5).