"Beating the market" is a difficult phrase to analyze. It can be used to refer to two different situations.
An investor, portfolio manager, fund or other investment specialist produces a better return than the market average. The market average can be calculated in many ways, but usually a benchmark – such as the S&P 500 or the Dow Jones Industrial Average index – is a good representation of the market average. If your returns exceed the percentage return of the chosen benchmark, you have beaten the market.
A company's earnings, sales or some other valuation metric is superior to that of other companies in its industry. How do you know when this happens? Well, if a company beats the market by a large amount, the financial news sources are usually pretty good at telling you. However, if you want to find out for yourself, you need to break out your calculator and request some information from the companies you want to measure. Many financial magazines do this sort of thing regularly for you - they'll have a section with a title like "Industry Leaders." We don't suggest you depend on magazines for your investment picks, but these publications may be a good place to start when looking for companies to research.