Depends how old...
ALWAYS, round dot inlays were done with an appropriately sized drill bit. If you have a CNC you might be inclined to interpolate the circle, but I think this is way overkill....
When I did more complicated inlays in my guitars, I cut the inlay (usually pearl) by hand, with a jeweler's saw. Then I put paint on the area of the inlay, and scribe the outline in the wood where I want to place the inlay.
Then I used a dremel with a router attachment and rout out as much as possible, cleaning up the sharp corners with an x-acto knife. (a lot of test fitting as well)
Then I would set the inlay with West System and sand/file the surface as needed.
When possible, it is always wise to get inlays pre-cut, because the delicate details often break off, necessitating cutting an entire new inlay... If you can get them pre-cut, it saves a lot of time and effort (which equals money).
Now, on cues, I will continue to use a bit for dots, and get assistance with a CNC mil to do pockets for diamonds. The corners of any sharp inlays still need to be cleaned up by hand...