1. Listen. Get to know what kind of spot the person wants. Do they want verbal encouragement? How soon do they want you to step in and help? Are you there only encase of complete failure or do they want you to help them get a few extra repetitions in? If they're using dumbbells, do they want a spot from the elbows or wrists? These are all questions you should ask before they begin the exercise.
2. Concentrate. While you're spotting someone, make sure 100% of your attention is devoted to them. Don't get distracted by anything interesting that's going on in the background, other people walking around or by talking to one of your friends. If anything goes wrong, you're the person that has to help. Looking around is only going to take away from your role as a spotter.
3. Offer Help. Some people find it difficult to ask for help. If you see someone looking around like they need help, offer a spot. If that's not what they're looking for, you can move on. If it is, your help will be greatly appreciated.
4. Just Say No. If someone asks you for a spot but you don't think you can handle the weight in an emergency, don't be afraid to say no. It's a lot easier to say no before you help than saying you can't lift the weight off in an emergency.
5. Help. A lot of people go into the gym for their first time and don't bother asking for a spot. They lift a lot more weight than they can handle and often can't get the weight off of themselves at the end of a set. If you see anyone in a situation similar to this, don't wait around and assume someone else will help.