There are a number of different ways to attach an on-camera monitor to a camera, but the most common method is to use a camera shoe mount adapter (like the SM103 from MustHD).
Typically, a shoe-mount adapter will screw into a ¼"-20 thread that’s built into the monitor (it’s common for on-camera monitors to have more than one ¼"-20 thread to give you more mounting options). The other end of the mount will be fastened to the camera’s hot shoe.
If you’re using a camera support rig with rails or other mounting points, the on-camera monitor can be attached in a number of different ways.