If you are doing business just under your legal name (for example J. Smith), you do not need to do anything - people just pay you. I have never looked into the legality of doing business that way, so you may want to check with a lawyer. If you do business under another name, in most states you'll need to register a DBA with that name. The DBA simply tells the state that legally you and the registered DBA name mean the same thing - you. And when you register that new name, it is protected within the state (usually just means that nobody else can use the same name for business).
There are a number of different legal entities you can use such as sole proprietor, limited partner, S-corp, C-corp, and of course Limited Liability Corp (LLC). Each of these has a different implication to your taxes, but of course, if the business revenue is fairly small, then the tax issues are also small, so it doesn't matter much. You may want to talk to an accountant to understand your best course of action with respect to taxes.
But the biggest reason you may want to consider using an LLC is for protection of your assets. If anyone were to sue because they felt your product, service or activities harmed them in some way (and keep in mind anyone can file a law suit at any time for any reason - it doesn't have to make sense), then it is best to have the protection of a business entity like an LLC. If you have an LLC (or a S-corp or C-corp), they cannot sue you personally, but can only sue the business. So if they win the lawsuit, they can only have what the business has. If, on the other hand, you do not have an LLC (or S-corp or C-corp), then they will sue you personally and can potentially win all your money, cars, house, anything you have. That protection is the biggest reason to form an LLC early in your company's development, even before you have customers. For all my ventures (except for the first one in the early 90's before they invented LLCs) I did create LLCs to protect myself and my family.
Best of luck!