Install and run Wireshark on your computer for a while. Occasionally, you will see ARP packets come by, and the "Info" section of the packet will say something along the lines of "Who has 192.168.1.x? Tell 192.168.1.100" (assuming that your network is in the 192.168.1.0 network). Shortly after, you should see a response from the computer with that IP address responding with "192.168.1.x is at XX:XX:XX:XX:XX:XX." If the IP address isn't on your network, you'll notice that the ARP packet instead asks for the MAC address of the default gateway, but a response is still received in that format.
That's basically how ARP works -- the sending host asks who owns a specified IP address and the host responds with its MAC address.
If you want more details (there really isn't a whole lot else left), you'll have to tell me what you've discovered so far about the protocol based on your research