All mine are just pressed together. For anything with a hex shaped or square shaped shaft I measure the diameter of the shaft (between the flats) and then use that as my drill size to drill out the handle. That way, when the shaft is pressed into the handle all the corners dig into the handle material and create a very tight fit that will hold securely.
The handles get clamped in place, and I drill them out using my drill press. I have found that cheap tile/glass/plastic paddle style drill bits work much better than regular HSS drill bits when drilling into clear handles. They are also very good at naturally self-centering when you are wanting to enlarge an existing handle hole. The self-centering feature is a definite lifesaver if you are trying to do all this with a hand drill, because you will have a much better chance of ending up with a straight hole.
For things like my little thumb bit holder and my short bit holder (that were originally round shafted) I just grind/notch lengthwise on the outside of the shaft so there is some "bite" for the screwdriver handle to grab. I make my notches by hand with a Dremel and a thin cutting wheel. You can visually see the final result by looking at my Williams rebrand ratcheting screwdriver shaft. Williams screwdrivers don't have any shaft finger knurling, so I made my own finger grip using the same technique.
I used the leftover screwdriver handle pieces to make the thumbwheels on my 1/4" socket extensions. I just drilled the screwdriver handle piece one or two drill sizes smaller than the extension shaft and then hammered it onto the extension. I do nothing to the extensions. The thumbwheels are only for quick finger loosening/tightening of bolts that spin too easily for a ratchet to function, so they don't need to be on there super tight. That being said I still can't make them budge using any force my bare hands can create. I have also made a few 3/8" drive extensions the same way, but I don't have any pictures of those at this time.