I've done a '91 Camry as well as an '01 Civic. Basically, there's a triangular plastic piece on the inside called a "garnish". Pop that off and there'll be three nuts on threaded posts. The other end of those threads are the pins you saw. You need to remove the nuts, remove the assembly (there's an electrical plug also that the mirror plugs into) and change the whole assembly. You may or may not have to remove the inner door panel to access the bottom nut, depending on the exact model.
The best price I found for a replacement was VIP. You'll need to have them order the mirror from their "crash parts" catalog. Expect to pay about $70 to $80.