Stippling can be done with a punch and light hammer, but most modern gunsmiths use a special power hammer hand piece for a Foredom Flex Shaft.
This is a hand piece that can be used to rivet, hammer, or stipple, depending on what point you put in the hand piece. It's used by jewelers, gunsmiths, and tool and die men.
This allows better control of the depth, or force of the stippling and that makes for a faster, more uniform job than doing it with a hand held punch and hammer.
The actual hand technique is to hold the punch between your fingers with the point slightly off the work.
When you strike the punch it impacts the work and leaves a dimple, then finger tension "rebounds" it off the work. By rapidly striking the punch and moving the punch over the area, you get the texture.
You can use any number of shapes of points on the punch from round, to square, to triangular, to a checkered end on a flat punch.
This isn't the only way to stipple or matte metal.
As example, famed gunsmith Armand Swenson did his famous slide top texturing by laying a new, large file on the surface and hitting it with a soft hammer. The file left the texture.