In the modern age of digital information, verifying a business license has become fairly easy. These licenses are granted by individual states, so you'll have to check with the state(s) where a business might be licensed. The procedure can vary by state as well, but the general process is the same.
Choose a state. A person is most likely to be licensed in the state in which she is doing business, but this might not always be the case, especially if the business activity crosses state lines. When in doubt, check states of previous or current residence as well.
Identify the licensing body. The name of the licensing body is different in each state. Sometimes it's the Department of Professional Regulation, the Division of Corporations, or the Department of Consumer Affairs. Usually a search for "business license" on the state's Secretary of State website will yield the appropriate link.
Search by name. Once you reach the licensing body, most states have an online search function that will go through their database and yield results on particular parameters. The easiest way to search, of course, is simply by the person's name. If he has a common name, though, this could yield a lot of search results that you'll have to wade through to verify against some other kind of information.
Search by license type. Another common parameter is the type of business license, often presented as a dropdown menu. Choose the best option based on the kinds of business in which a person engages. Sometimes this will be a discrete search option, while in other states it might be one of a series of options designed to narrow a search.
Search by license number. A less common but no less important search parameter is a search by license number. It's not unusual for a professional contractor to include her license number on vehicles or other advertisements. A search by number can verify that the number is valid, current and assigned to that individual.
Warnings
Not finding a business license doesn't necessarily mean a person or business isn't licensed. It might be that the license is in someone else's name or a different legal name, registered with a different state or of an unexpected type. The more information you have about the person you're searching, the more likely you are to find his license.