economics of public goods

I'm sure lots of people more competent in economics have worked this out before, but I want to work it out for myself.

Scenario: there's something that lots of people (for simplicity, let's assume everybody in a given town) wants, which by its nature will benefit either everybody (if it's built/bought) or nobody (if it isn't). For example, a fire engine, a water treatment plant, an additional police officer, an emergency room, etc. However, the town in question is in New Hampshire, and extremely suspicious of taxes and big government, so they want to build/buy the thing with voluntary donations. Under what circumstances will it actually happen?

( armchair economist analysis )