The right term is the hanging drop method. It's usually used to study motility in bacteria or any other microorganism.
You use a special glass slide called a cavity slide for this. It has a circular concavity in the center. A droplet of the suspension of the microorganism you want to study is place on the center of a cover slip and then put a line or dots of petroleum jelly (Vaseline) along the edge of the slip. The cavity slide is then inverted over the slip so that the cavity side is down and over the droplet on the cover slip.
The jelly holds the cover slip in place. Turn the slide over and the droplet should hang from the cover slip into the depression. You can now mount this slide on a microscope and observe the specimen.
You can also use the hanging drop method as an alternative to the wet mount since the wet mounts tend to dry quickly.