Stabilizing mounts are used to film Smooth moving shot in Motion Picture Cameras, these mounts may transform depend on places and situations. In the early days Video camera men and directors have two choices for Moving shots such as Camera dolly and Hold the camera in his hands, but those cannot prevent the image from shaking. Stabilizing Mount have changed the dimension, its stopped jerks, bumps, and shakes in cinematography and videography.
For Further please refer Wikipedia
Most frequent Stabilizing mounts:
MMC / Mini-Motioncam
Shoulder Rig / Shoulder Mount
CineSlider / Dolly
Note: People like me even use mono pad as Stabilizer mount
However choice of stabilizer may change according to purpose, but Steadicam (full hit) cover most of the above stabilizer's features perhaps i have linked the Professionals way of using Steadicam videos below.