The two simplest structures to set up are a sole proprietorship or a general partnership. Simpler as you will see below is not necessarily better.
For a sole proprietorship, in the United States, you should check with your county government office to obtain the details of registration. If you are in an area of low risk, and your advice or work is not likely to be associated with substantial liability this may be just the structure for you. It is best to check with a lawyer. As a sole proprietor, there is no difference between your personal liability and that of your business.
You could form a general partnership with a colleague who has complementary or similar skills. If the demand for your services is more than you can handle, having a partner could be an attractive option. The rate at which work comes in may be uneven, and your partner could step in when you are too busy. You may even like to go on vacation without having to say no to new projects, or working through your “time off.” Sounds good, doesn’t it? The problem, though, with general partnerships is that from a liability point of view, there is no difference between you, your partner or your business. This is even worse than a sole proprietorship. You would be better off having someone else take care of the business side, including liability insurance, than have a sole proprietorship or general partnership.