If you don’t have hole punch pliers (which is the tool designed for the job and used by tailors and seamstresses), you can use a variety of substitutes as others have pointed out: drill bits, nails, awls, etc.
One of my favorites is a short section of metal tube, like small diameter brake line or fuel line. I file a nice bevel on one end so that it’s a fairly sharp edge which I then set on the belt at the appropriate spot, then whack the other end of the tube with a hammer to punch out a nice, clean hole.
Fabric belts typically need some kind of reinforcement around the new hole. This could be stitching around the opening, or you could get a small grommet or eyelet and press those in to keep the hole from being enlarged over time.
