A porcelain sink with a crack in it can be repaired within a couple of days. The only tools required are cleaning supplies, fine sandpaper, commercial epoxy adhesive, a pair of rubber gloves and appliance paint.
First, clean and dry the crack and the surrounding area thoroughly. Using a toothpick, carefully fill the crack with the epoxy adhesive, and leave it to dry for at least 24 hours. Wear rubber gloves when handling this adhesive. Once the epoxy has fully dried, sand it to smooth the edges, and paint it with appliance paint that matches the color of the sink.