Typically it is done two ways.
1. You take a caribiner and using either gaff or black tie line, you attach it to the triax in a spot that allows you enough slack to move the camera freely. Then attach caribiner to you your belt, not a belt loop. Black tie line is preferred and much less messy than gaff.
2. With Steadicam there are different methods of hanging the cable from the camera, but 99% of the ops use a jumper cable that is thinner and lighter to go from the camera to a connection that is attached to their vest between their jumper and the main line. This is true for triax or fiber. Most of the time, it is a caribiner to the vest for quick disconnect. There are variations on this process that are debated on the forum, but this is the basic set up description.
John