Some were held in with small screws, as seen on early 1800s guns in Massachusetts. Others were held by brads with hidden heads. If you look at my profile pic, all 6 stars have one, and the eagle has 5. Here's how I made them, using #18 brass brads (for brass inlays):
1) drill a hole in a piece of steel the diameter of the brads. Flare the hole with a larger drill bit to add a countersink as big in diameter as the brad heads
2) place brad in the hole, peen the head into the countersink to fill it
3) drill and countersink a hole in your inlay, drill a smaller pilot hole in the wood itself
4) cut the brad shorter if needed, 3/8" to 1/2" is plenty long; cut diagonally to give it a pointed tip
5) drive brad into inlay and fill countersinkb gently peen a bit if needed
6) file head flush with inlay, polish up with fine sandpaper
If done right, the brads will be virtually invisible. Here's a hunter's star done the same way.