Many self-employed people will run their business as a sole-proprietorship. They are very easy to set up and cost very little to form.
First, decide on a name. For example, John Jones D/B/A (Doing Business As) Prime Time Painters. Then register your name with Town Hall. Get some business cards, letterhead and stationary. You are now well on your way.
We live in litigious society. Businesses that are organized as sole proprietorships are taking on unnecessary risks.