Unlike most kitchen sinks, which drop into a hole cut in the countertop and are supported by the countertop and cabinets below, an apron-front sink slides into an opening or gap in a countertop and is supported by the base cabinet only. A large porcelain sink can weigh 300 pounds when filled with water, so supports must be added to the cabinet to carry this weight.
Measure the "true" height of the sink, from where its top aligns with the countertop surface to the bottom of the sink’s sides, which will rest on the supports.
Transfer this measurement to the interior cabinet sides and mark a level line from back to front. This is where the supports will be added to carry the weight of the sink.
On each cabinet side, install 2x4 supports. Position the tops of the supports even with the level lines. Use construction adhesive and 1-5/8" square-drive deck screws to attach the supports. Apply the adhesive first and clamp the supports firmly in place, then drive the screws through the cabinet sides into each support.
Measure the height of the sink front, and add 1/8” to this dimension when you mark the base cabinet front cutout. This allows the sink to rest just above the cut edge, without being supported by it. Depending on your base cabinet, it may be necessary to remove the doors and replace them with smaller doors.
Use a jig saw to cut out the sink-front opening.
Test-fit the sink in the opening. The entire weight of the sink should be carried by the side supports. Check that the sink is level from side to side and front to back. Add tapered wood shims to adjust, if necessary.
Install the sink and use silicone caulk to fill in the gaps below the sink front, and between the sink and countertop.