I somehow forgot exactly how I did the holes in my last saw handles, and I just had to do it again, so I’ll enumerate the steps so that I don’t have to remember the next time. Basically, you need to bore holes in the handle, with one side of the handle having larger holes than the other, because one side needs to house the saw nut, which is wider than the screw on the other side.
So here’s how (it assumes that you’ve already cut the sawblade kerf):
1. Secure the handle with a sacrificial board underneath.
2. Mark the holes on the screw side with an awl, using a template (or by hand).
3. Drill all the way through with a brace and bit sized for the screw.
4. Clean out the holes and sawblade kerf, flip over the handle, and resecure.
5. Place a piece of paper in the sawblade kerf.
6. Using a twist bit sized to the saw nut in the brace, enlarge the holes on the other side. Slowly ease your way in to prevent tearout and keep the hole centered.
7. Stop when you hit the paper. After enlarging all of the holes, pull out the paper and clean out the sawblade kerf again.
8. If necessary (this depends on your hardware), carefully use a countersink to countersink the holes on either side.
I suppose that it isn’t strictly necessary to have different-sized holes with the hardware that I’m using, but you definitely need to do it with older-style saw screws and nuts.