I'm in the opposite position- I'm a sound guy that's just learning to shoot video. I'm also a videographer on a very tight budget [no budget], so I've learned some tricks that help me get better results using the on-camera mic.
Gasp! you can't do that, right? I'm sure every other article you've read has told you to go out and buy a. a Rode videomic or b. a Sony field recorder, and until you do that, you're sunk. The truth is that there's a lot you can improve while you save up your nickels and dimes for better tools.
While Shooting:Listen to the environment and adapt. Your ears are great at filtering out unimportant noise. Your camera is terrible at it. Listen for loud fans, rushing rivers, people talking, etc, and when they get in the way, move!
Put the camera uncomfortably close to an interviewee. With a 50mm prime lens, I get decent audio level when I frame only their face. This still picks up the acoustics of whatever space you're using, so it's not perfect, but it is a start.
Use a backup. I've been known to use an iPod touch as a backup recorder, just in case there's something wrong with the camera audio. if you need to use it, carefully watch the consonants or any fast, sharp noises to help you sync it perfectly.
While Editing:Watch your meters. The audio meters tell you how loud the sound is in relation to a standard voltage called "unity". Unity is marked on audio meters as the number 0 or the letter U. You want your audio to peak at unity unless you have a specific reason for it to be louder or quieter. Under NO circumstance should you let it hit the top of the meter, even for an instant. To help you with that, some video editors (like FC express) have a "peak hold" feature, which leaves a red light on at the top of the meter if the audio clipped at any point in time. If you see that light, go back and find the problem.
Use SFX. Now, things can get real cheesy in a hurry, so be careful to do this tastefully. A little [emphasis on little] wind noise adds a sense of atmosphere to your outdoor video, and helps to smooth out the transitions between audio clips. It creates a bed of soft noise that your important audio can rise out of and fall away into. Remember how carefully you listened to the environment while shooting? At this stage you can add back in the ambient sounds that you liked. I like using freesound.org for these basic sounds.
Use filters to remove unwanted noise. Are fans or wind noises ruining your spoken parts? A male human voice goes down to about 120 Hz at its lowest, so you can remove low sounds by filtering out everything that's below human vocal range. It will leave the dialogue untouched. This filter is called a High-Pass filter.
Just listen. Usually before exporting a video, I will let it play with my eyes closed. The audio should be able to tell much of the story by itself, after all it is more than half of your video. Just listening will help you hear all of the awkward audio transitions that you missed while you were admiring your brilliant cinematography.
Of course, these are very basic tips. Have a specific question? Feel free to ask.