Istrasci's answer is basically right and deserving of the green check, but I thought it worth adding a little more dimension, which is to answer a question implied by yours, which is, "how do Japanese people approach the problem?" (Not to mention that Stack Exchange considers a healthy site one that has more than one answer to each question...)
There is no particularly reliable system for determining what reading to use for a person's name. However, there are a lot of very common readings associated with the most frequent names. As one friend described it to me, in a sense, people in Japan have a memorized list of the most common readings that they will use as their first guess.
田中 is most likely to be
たうち, or other possibilities, for no other reason other than it's the usual reading.
If you look at a lot of people's name cards, they will often have furigana over their names, either because it's a common kanji with an unusual reading, or a kanji that is so unusual that they don't expect most people to know it. It's an indication of how Japanese don't expect anyone to be able to determine a reading by another other method other than simply being informed of it.
People born and raised in Japan simply have the benefit of familiarity. As someone who is not native to Japan but have lived here a long time, I've built up my own list of assumed readings, though of course it's not as reliable as the natives.
Ultimately, it's not something you need to really set out to solve. The longer you deal in Japanese, you'll naturally just become familiar with the common readings. And no one is surprised or offended should you ever have to ask for a reading.