I had the same thing happen to an Intellimouse Explorer (optical). If I remember correctly, the mouse button makes contact with a very small point. This point depresses a small whitish button enclosed in a black box. The box contains a copperish-metal post on each side, and a slightly curved piece of metal suspended between the two. The whitish button bends the curved piece enough to make contact with a notch on one of the posts, then snaps back. That is your *click* sound.
If you have good eyes, and a jeweler's screwdriver (or something small enough to align things with) you can do it in about 10 minutes. If you drop that curved metal piece, expect it to take an hour.
Oh, and this has to win the "thingamajig award for in-depth technical explanation"...