Open your video with a native video editing program on your computer. Possible programs include Windows Movie Maker, Adobe Premiere, and on the Macintosh you can use iMovie.
Use the "File" menu to "Export" the file as an audio track. Select either "WAV" or "MP3" as the destination format. WAV files are higher-quality files, but they also take up more disk space.
Drag the audio file into your audio editing program. This will import the audio and prepare it for processing.
Select the "Effect" menu and choose "Remove Noise" from the drop-down menu. Highlight three seconds of the audio that consists of noise only, select "Get Noise Profile" and then click "OK." Choose the "Remove Noise" option again and press "OK." This will remove noise from your audio file.
Save the audio file to your desktop. Remove the original audio track from your video editing program by selecting the audio track and pressing "Delete" or "Backspace." Drag the new audio file into the video editing program and "Export" the file as a video file of your choice.