I generally grab either the stick or leather tab based on what type you have between my thumb and index finger and push said tab or stick straight down into my rear pocket. Is there another way?
Inserting the stick in the wrong... umm... "aperture" back there? J/K!!
Seriously, I'd used one of those pocket chalkers for years. I have the CueTec one that looks like the first six inches of a cue shaft (with tip and ferrule), and has the Tip-Pik built-in:
The problem I had with this one, is having it "gloss by" the edge of my rear pocket -- while trying to blindly insert it into my rear pocket, it wouldn't catch the lip of the pocket, and I'd have to finagle a bit to get it to "catch" and slide into the pocket.
One of those "bullet" chalkers -- with the replica of a .308 Winchester rifle cartridge, like this one:
...would've been better, because the bullet's "point" would catch the edge of the pocket a lot easier than the dull/blunt end of the CueTec's pool cue replica.
However, the issue is now moot, because I find *this* chalker to be a lot easier and quicker to use:
What's nice about this one, is that the little metal clamp that goes on the chalk cube itself, has a low profile, so you can wear your cube of chalk down really low -- past half-way -- before the metal clamp itself starts to rise above the height of the sides of the cube.
The other [pocket] chalkers shown above, have a little plastic cup for the cube of chalk that gets in the way once you start wearing the cube down past, say, an eighth of an inch of the original height.
All of this, of course, assumes you're chalking correctly by swiping the chalk on the tip, and not drilling a hole in it.
Hope this is helpful!
-Sean