How does the rooster fertilize the egg?

Excuse me, could you please clarify the process by which a rooster fertilizes an egg? I understand that reproduction in chickens involves both the hen and the rooster, but I'm not entirely sure about the specifics of how the rooster contributes to the fertilization process. Could you walk me through the steps, from the moment the rooster and hen mate, to the point where the fertilized egg is laid? I'm particularly interested in understanding the biological mechanisms at play. Thank you for your time and patience.