The main actuator for a coin-operated gumball machine is the horizontal crank on the outside which usually has a coin slot at its base. When the correct type of coin (as judged by size and weight) is put into the slot, it depresses a small lever inside the coin slot which allows the crank to turn. Without a coin, the crank can not turn to engage the internal disk.
As the external crank moves, the gears on its horizontal axle turn a vertical axle. When this vertical axle turns, it causes a disk at its top to rotate. This disk has a small hole in it to allow a single (or sometimes multiple) gumballs to pass through.
The gum balls are held in a hopper; a large holding tank at the top of the machine. When the disk which holds them in place turns, a small hole in the disk rotates, allowing a gumball to pass through into a small tube or slide. The gumball is pulled by gravity down the slide until it exits the gumball machine. This can be as simple as a slide a few inches long ending at a weighted, metal door that the customer opens to retrieve their gumball, or can be a complex slide that is several feet in length and which causes the gumball to do loops, jumps, or spins before finally being vended to the customer.