Verify that bribery is customary in the country you'll be traveling through. The X-rated magazine you proffered up to get you past a Mexican army checkpoint would get you imprisoned in a communist country. Travel guidebooks are typically good sources of information about dealing with foreign officials.
Determine who is in charge before offering a bribe. If you deal with anyone other than the superior, you may offend him and create a face-losing confrontation. Be extremely careful not to insult or upset anyone.
Identify exactly what the problem is. If you're in violation of some law, ask to pay the fine on the spot. If you're carrying something they want, offer some of it. Your ultimate goal is to agree with the official on both the problem and a mutually beneficial solution.
Offer a legitimate explanation for the bribery to put a veneer of legality to the situation. For example, say that you're afraid the fine will get lost in the mail and that you'd rather pay the proper authorities right now. The way in which you offer a bribe is sometimes more important than the bribe itself.
