The Atlantic Wire has a good article called Proper Etiquette for When You’re Under Arrest. My friend and fellow attorney Dietrich Epperson is quoted in the piece. The article highlights one of the few times someone may plan on getting arrested. When engaging in protests, arrests are fairly common even for people who haven’t done anything illegal.
It’s worth reading the whole article, but the first two points it makes are particularly important: be polite, respectful, and professional with the police, even if they’re being jerks to you, but don’t say anything that you don’t have to. These points may seem at odds, but they really aren’t. You can politely tell the police that you aren’t going to answer their questions. In Utah, you’re required to give your name and some identification. The article also recommends that you supply your address and your social security number if the police ask for it, but beyond that, you really want to have an attorney present for any and all questioning.