Publicly traded companies (meaning that their stock is traded on a stock exchange) are required by securities law to publish financial information. If that's your competition, then you have a head start, but they can also bury the specific information about a specific location in a lot of other information, so it's not always easy, even then.
If your competitors are not publicly traded, then they have no legal obligation to tell you anything. So you can ask them outright, or research them. How to research them is hard to generalize, but sometimes you can find published interviews where they talk about how many employees, for example, and you can extrapolate revenues from numbers of employees. See what's on their website, look for things like Alexa.com visits or something for their websites (not reliable completely, but good enough for an estimated guess). If they are brick and mortar stores, it's legal to shop them, ask questions, park outside and count customers, and then make more guesses.
Tim Berry is the chairman of Eugene, Ore.-Palo Alto Software, which produces business-planning software. He founded Bplans.com and wrote The Plan-As-You-Go Business Plan, published by Entrepreneur Press. Berry is also a co-founder of HavePresence.com, a leader in a local angel-investment group and a judge of international business-plan competitions.