This is every bargain hunter's dream scenario. You don't give me any clues as to how 'well-known' this artist is. Paintings by the likes of Pablo Picasso, Renoir, Frederic Remington, Marc Chagall etc., are almost impossible to authenticate and sell without either excellent, provable provenance, or detailed research by an art professional. If, however, your painting is worth somewhere between $500 and $10,000, which is still a handsome sum, you can just present yourself and your item to an auction house or art dealer and get their advice. Paintings by high-value artists need to be referred to one of the more high-end auctioneers such as Sotheby's, Christie's etc. If this is your likely route, email your inquiry to the auction house including good quality photos of the picture both front and back with close-ups of any labels, chalk marks, written notes on the frame, or other distinguishing features.