Graininess is typically as a result of the camera auto-adjusting it's "noise" level to compensate for low light conditions. Was this footage taken in low-light? Perhaps indoors? Was you perhaps shooting into shadow?
If the answer to the above is no and in fact you was shooting in good light then get your camcorder's manual and ensure that you haven't set the "noise" level inadvertently, or enabled some low light setting on an auto-programme.
I am afraid there really isn't a whole lot you can do regarding footage you have taken. I would look in your software and see if you have any video clean up filters. Failing that, perhaps take a look on the net for some "clean video" "plugin. You could also perhaps try adjusting the brightness, contrast, saturation settings, but I wouldn't expect a dramatic improvement.