Articles are sometimes the most difficult thing about English, especially for non-native speakers. Here are some basic guidelines:
Use the when you want to be specific about a noun; use a when you want a more general reference.
Compare: the president (the one we both know I’m referring to) or a president (any president, no one in particular).
You would rarely use a before a proper noun because the name itself is a specific identifier. For example, you would not say, “May I introduce you to a Tom Selleck?”
You would, however, use the when you want to emphasize that the proper noun is the one everyone thinks of when they hear the name. For example, I once received an email from someone named Gary Larson. I had to ask, “Are you the Gary Larson?” I was referring to the comic artist, and he was not that talented person, but he does have his own talent and a very useful writing site at http://home.comcast.net/~garbl/.
There is the rare time when you might want to use a in a way such as this: He was in touch with a Dr. Kevorkian, but I don’t know why. Obviously, the speaker does not know the doctor’s reputation but expects that the name would have prominence in some circles.
There are many excellent online sources for this very subject; here’s one I like: http://www.ccp.rpi.edu/resources/handouts/nnes-esl-students/article-usage/.