Here is one of the best ways that you can most quickly improve audio quality, almost across the board, taking amateur sound to professional sound on videos.
For some reason it just seems to get ignored. I preach from this soapbox a lot. See my post Audio For Videos: Do Not Let Bad Sound Ruin Great Video.
It really is as simple as this - get the mic closer to your mouth.
The reason so many videos sound bad - especailly "talking-head" videos, is that the mic is so far away from the microphone. People usually use the built-in microphone on the camera, which is not only many feet away from your mouth, but is also usually not a very good microphone.
One way to get that microphone closer to your mouth while shooting video is to use a shotgun microphone. You often see sound guys on TV and movie sets holding a long pole with a microphone on the end of it just over the speaker's head. Those are usually shotgun mics.
Well, Sennheiser, maker of excellent quality microphones and headphones (see my review of the Sennheiser MKH 416 shotgun mic - my "desert island" mic), has been running a series of video tutorials on getting good audio quality on videos. See the first video below, where they talk about shogun mics like the MKH 416, as well as other kinds of mics good for video production.