Antique paintings can be quite lucrative and easy to sell, but there are a few things you must learn about art in order to maximize your profits. You should also keep in mind that it is extremely unlikely that you will have a piece by a renowned master, so expect a modest profit in the range of a few hundred to a few thousand dollars, depending on the artist, style, period and history of a piece. Documentation that can help prove a piece's background can also help to drive up the price, so hold on to any paperwork you have.
Find out who the artist is. This is not always possible, but usually you will find a name in one of the bottom front corners of the painting or on the back. Some artists also mark their names on the sides of canvases or hide their signature in the work, for example in the shadows under the subject's foot. After you learn who the artist is, you can research her to learn how valuable her work is and the value of potential "new" (newly found) art. Some little-known artists are not valuable in and of themselves but may still be collectible because of their style or period.
Identify the period and style of the art. These usually go hand in hand, such as abstract work in the 1970s, but it is not always the case. Look for the date on the piece if there is one and research art from that year. If you do an image search online, you should be able to see what paintings are done in a similar style. Look up the name of the style in which those paintings are done to learn about the style of the piece.
Appraise the piece. To do this, take the painting to a professional appraiser (or email him an image). The reason for researching before doing this is that while uncommon, it has been known for the owners of very valuable paintings to be tricked into selling their paintings by unscrupolous appraisers. Researching will give you an idea of what to expect, but an appraisal is important, particularly for more valued artists or styles, because they can find unique aspects (and flaws) in your painting that will affect the price, which may make you more money. The appraiser will also file paperwork and document the origins of a painting, which will make it more valuable in the future by showing a clear line of provenance.
Sell your art. There are a variety of ways to do this, from eBay, if you are willing to accept less and do the legwork yourself, to estate sales and auction houses. There are also galleries and museums that will buy art that is verifiable and valuable, but your best bet for selling to them is to approach an art buyer or participate in an auction with a prestigious auction house that specializes in art.