Recently my kids traveled as UMs on a domestic trip with a connection. I'd assume that the process would be quite same on international trips as well.
When I tried to book the ticket on website the system wouldn't allow me to book as it detected travelers as minors based on DOB.
I called the DM line and was told to go ahead and complete the booking with different DOB which will make them adults, after completing the booking I gave confirmation number to DM agent and she fixed the DOB to actual year and then handed me off to UM reservation agent where I was asked for contact number and identification details (driving license number) of persons dropping off and receiving the kids and also their address. I was also prompted to select a 4 digit pin number and was told that any future changes will only be made after confirming this pin number from the caller.

On day of travel we went to special service desk (can't check in minors online) and their wristbands were printed with bar codes and a sealed envelop was given to me with their BPs stapled on it. At the gate I handed this envelop to GA and she took them in even before the pre-boards. At the connection point they remain on board with an FA until everyone had deplaned and then they were taken out and handed to GA who then handed them off to another delta employee who took them to their connecting gate and handed them off to the GA there.

At the destination airport, receiving person had to go to special services desk where his details - cell number, DL number and address were verified and they were given a gate pass to go past security and meet them at the gate.

Added: Please note that any changes to pick up person at the destination point have to be made before you start the journey and UM reservation line agents will not allow any change after the journey has started so be very sure about who will pick them up before you get their details into the system