A sole proprietorship is a company with one owner that is not registered with the state as a limited liability company (LLC) or a corporation. In some states, a sole proprietorship is referred to as a DBA (doing business as), as in "José Smith, doing business as Smith Heating and Air Conditioning."
Establishing a sole proprietorship is cheap and relatively uncomplicated. You don't have to file any papers to set it up -- you create a sole proprietorship just by going into business. In other words, if you'll be the only owner of the business you're starting, your business will automatically be a sole proprietorship, unless you incorporate it or organize it as an LLC. Of course, you do have to get the same business licenses and permits as any other company that goes into the same business.
To learn more about this kind of business, see Sole Proprietorship Basics.