Wrap a piece of string around the portion of the sink you wish to have at the counter height, with the rest sitting below the counter. Mark on the string where the end of the string overlaps the rest of the string.
Measure from the end of the string to where you marked on the string, telling you the circumference of that portion of the sink. Measure the exact center of the counter and place a carpenter’s compass post in the middle; then use the compass to draw a circle the same circumference as you measured on the sink.
Drill a hole near the edge of the circle you traced on the counter. Use a jigsaw to cut along the line you traced with the compass.
Place the sink in the cutout, and lay a level across the sink. Reposition the sink until it sits level; spread an even bead of silicone bathroom caulk where the sink meets the counter. Allow the sink to sit undisturbed for at least 24 hours, letting the caulk fully cure. This means you should not install the faucet, water supply lines or drainpipes during this period.