Larry's right...older cars with studs coming out of the back side of the emblem had holes drilled in the sheet metal to the same stud pattern. They either used barrel clips which are small tubular clips that push in the hole and they have tiny little fingers that grip the hole and the studs on the emblems. Some emblems with larger studs used self threading nuts that held onto the studs from behind the sheetmetal. If you choose to, you can carefully snap off the studs and apply them with double faced tape made for that purpose although it's not correct. Just make sure they're in the right spot on the car and level.
If they are original emblems they used grip inserts that are pushed into the holes. Either you're adding extra emblems or someone previously filled the holes with filler before painting. Properly restored condition would require origanal equip.