Any advice about cleaning an oil painting that's covered in dust or yellowed varnish must come with a major disclaimer. More than other kinds of do-it-yourself projects, cleaning oil paintings should really be trusted to expert conservators. Furthermore, altering true antiques almost always decreases their value, whether or not they look better to you. If your painting is not that old, not terribly valuable, or not too important, however, there are a few possible ways to make it look brighter and cleaner yourself.
Before the 1940s, paintings of oil on canvas were frequently covered with a layer of varnish to add sheen and protect the thick layer of paint, called the impasto. Yet varnish reacts differently to the environment than does paint, so these varnish seals end up cracking, yellowing, or gumming up over time. It can make the original hue of the oil paints look dull or discolored.
If it seems that your painting is older, assess whether the paint is in good shape but the varnish has aged. In this case, try applying a mild solvent called a conservation liquid. Art supply stores might sell an "emulsion" designed to clean and remove varnish. There is always a chance that the solvent will also damage or remove the oil paint. If you are willing to risk this possibility, dab the emulsion with a cotton swab very delicately. Try spot-testing one corner before moving on to the entire canvas. Work in an area with adequate ventilation.
For recent paintings, your problem is more likely a build-up of dust, smoke, pet hair, dander, and even bacterial or fungal growth. In this case, make sure none of the paint is ready to come off the canvas or board, meaning that it doesn't exhibit any cracks or flakes. Then you can carefully dust the surface with a very soft, dry bristle brush, such as a baby toothbrush or shaving cream brush.
If the surface is sticky, grimy, or oily, you may want to take the cleaning a step further and actually use a mild detergent solution. Again, generally speaking, oil and water should never mix, as moisture can damage both the canvas and the impasto. Proceeding with caution, use brand new cotton cloths dipped in a mixture of dish soap and warm water. Lightly blot the surface, but don't scrub, wipe, or rub at the painting. At no point should you submerge any part of the painting, nor allow so much moisture that it drips or pools.
For the experimental types, people have come up with some unorthodox methods of getting dirt off an oil painting. White bread seems to work. Ball up soft, sticky, doughy white bread and gently rub it against the canvas. You'll see it blacken like a pencil eraser. Brush off the crumbs. You also might try a low-suction vacuum with a brush nozzle. This should remove pet hair and dust balls in a deeply textured painting.