Tracking down the artist of a painting can be enjoyable or frustrating, easy or impossible. It all depends on how much information you have up front and how much time you have on your hands. The history of art is littered with stories of lost masterpieces that have hung above a fireplace or collected dust in an attic for centuries, and these stories still pop up today. If you have a painting by an unidentified artist, be advised from the start that it is not likely to be a Rembrandt, but if you are interested in learning more about it there are a few steps to get you going in the right direction.
Ask the source of the painting, the person who provided it to you, if he knows who the artist is or where the painting came from. This is obviously the simplest way to identify and learn more about the artist. A gallery will have comprehensive information on artists they represent. A friend or family member may be able to give you a thread of information you can begin to unravel.
Search the painting for a signature. Not all artists sign their work on the front of the painting anymore, and some do not sign their work at all, so do a detailed search. Look at the back of the painting and examine the sides. Take it out of the frame, if it is framed, but use care. Check all unpainted areas of the canvas or painted material for a name, signature or writing of any kind. Look also for any pencil or other marks, or any identifying papers that may be attached to the back of the painting, such as a gallery stamp or an exhibition receipt. These things may lead you to people who know something about the painting.
Seek out the help of a professional. An auction house may be able to identify the artist on sight, or point you in the right direction. Museum curators or persons working in local art organizations may know something about it, especially if it has a regional theme that corresponds to your area. You may find yourself putting together many pieces of information to get your answer, much in the manner of a mystery.