JoeSMG
and have some type of conveyor belt.
Typically just rails, either bulb-top "T" or full round fixed to the deck.
Dedicated minelayers have a "downhill" slope at the end of the track. So, you roll the device on its wheels to the end, and put it on a stop chain. Then, when the bridge office indicates, the pelican hook is opened and the device rolls over the stern. The 15-20 deck apes hunkering about on the Sea Detail, then heave the stack out so the next one is ready in the stops.
This can alternate port and starboard to need.
Unlike in the movies, where the things are strewn about willy-nilly maybe 300-400 feet apart. You lay mine fields in a grid about around the length of the target vessel. So, they are laid around 300-400 yards to around 600-800 yards apart. The spacing also needs to be wide enough that the devices do not foul each other due to currents & tides, or storms.
The minelayer will get to the end of the line, and turn down the last line run, and make the next grid line. Floating mines stay attached to their anchor by way of a salt plug to keep the field "safe" until the minelayer can get out. There is some considerable navigation required to lay the grid lines.