If you get accepted, you have to reply to their offer by May 1. The reply can either be a yes, no or a request for a year's deferment (which they always grant). It's the same scenario with most universities. I don't know about Princeton but you'll reply through an online form for most universities (like Yale, for me).
Edit 1: check Princeton's admissions site for more details, but there's not really much else to this
It's a pretty simple and non-scary process