An Incident light meter reading measures the light falling onto a subject instead of the light reflected by it. An Incident meter reading is far more accurate than your camera's own light meter but it's nowhere near as convenient.
How To Use A Light Meter (Part 1) we looked at what happens with the camera's own reflective meter is presented with things which reflect different amounts of light so you'll know what to expect when it gets it wrong.
To fix the problem all you have to do is alter your exposure from what the camera says is correct - to the one that actually is. You can do this either manually or if your shooting in a semi auto mode you can use the exposure compensation http://www.photographycourses.biz/exposure_compensation.html which is what I'd do.
Don't be afraid to overrule your camera's light meter when confronted by mostly bright or dark subjects. Digital is so easy you can shoot a couple of test shots and if they don't look right - change the exposure and ignore the light meter telling you it's wrong.
Mike Browne