Most likely, the painting is simply dirty. If it's acrylic on canvas (you're sure about that, right?), you can try simple soap and water. Dab at it lightly with a lint-free rag. Don't scrub, don't get it soaked, don't leave soap on it. And try the inconspicuous areas (say, behind the rabbet of the frame) first, just to be sure.
If it's not just simple surface grime, a more thorough cleaning would involve stripping the old varnish layer, and re-varnishing. You probably want to leave that job to a professional, especially if you're not sure whether or not the painting is varnished, or with what. To find a professional conservator, I'd suggest asking at museums and galleries in your area, or you might try