Every so often, a project falls into your lap that is less than ideal. Perhaps you weren't behind the camera, but a friend asks if you could edit a short video of their holiday party. You accepted, of course, but within moments of viewing the poorly-lit, grainy footage, you wish you hadn't. As an editor, you're not always in control of the video you work with.
Fortunately, you and your computer can salvage footage that is seemingly beyond help. One of the reasons dark and grainy video looks bad is because the colors lack saturation. This leaves the images looking muddy. By removing the color information from the video, you are removing part of the problem. You can do this by using a black-and-white filter, or by using the color correction tool to remove the color saturation. This will help in minimizing the grainy look, as well as give the video a old-movie feel.
If you can't afford to go black and white, reducing color saturation will still aid your visuals. You can build upon the old-movie theme by using a strobe effect, which will add a flicker to the video. As for the sound of your given footage, this may be the most important part to fix. Clean audio can save the day, and that's exactly what you'll want to do, clean up the audio. Most editing programs have low-cut or high-pass filters, and these can be used to automatically adjust the tones in the video.
To adjust specific sounds, look for digital noise reduction. The process here is honing in on a sample of sound that you do not want, then the feature will recognize that frequency within the clip and lower it. The difference in your waveforms should be like the ones in the image above. Don't give up hope on bad footage just yet. Bad footage doesn't mean your project is doomed. With the proper editing techniques and some creativity, you can turn a hopeless project into a video that doesn't disappoint.
For more tips on how to work with bad footage check out Fix It in Post.