Fertilization is the process by which an egg and sperm fuse together to form a single cell called a zygote. It begins when a sperm contacts and attaches to the outer surface of an egg. The sperm then penetrates the egg's coating and its nucleus fuses with the egg's nucleus. This fusion of the sperm and egg nuclei marks the completion of fertilization and allows their chromosomes to mix, forming a zygote which then develops into an embryo. The key steps are the sperm attaching to and penetrating the egg, fusing of their membranes, and finally fusing their nuclei.