Computer A compares its IP address to Computer B's IP address using the subnet mask. They have matching network IDs, so Computer A sends an ARP broadcast to determine Computer B's MAC address. Computer B responds with its MAC address, allowing communication. When sending to Computer C, their network IDs do not match, so Computer A sends the packet to the default gateway instead of directly to Computer C. Subnet masks in binary and dotted decimal format are used to determine if the IP addresses have matching network IDs.