Hands out IPs yipee.
New device will use DHCP DISCOVER to find DHCP server.
Once a DHCP is found it will acknowledge the flair signal sent out by the device like a hunter in monster hunter world hahahaha and it will reply with DHCP OFFER which is the server providing an IP address.
The device with no IP and a cup saying "spare IPs?" sees the offer and says "yes!" and sends over a DHCP REQUEST accepting the offered IP address and will begin using it.
The DHCP server acknowledges the accepted IP address offer and sends over the DHCP ACK and the lease time (nothings forever).