The first (and easiest) problem to fix is that of varying levels in your audio file, both within certain scenes (say, a wedding ceremony) and from scene to scene (perhaps from the ceremony to the reception). Here's a common scenario. You've mic'd the pastor at the wedding, and she comes through fine, as do both the music and especially the applause at the end. But the bride is either having second thoughts or is so tightly bound in her wedding dress that her vows are a muted whisper.
An editor's first thought is often to "normalize" the entire audio file from the ceremony. Briefly put, during normalization the audio software boosts volume so that the loudest sample reaches a defined level, usually labelled 100%. This ensures the widest available dynamic range without introducing distortion or clipping. Sounds perfect, doesn't it? No muss, no fuss, and NLEs like Premiere Pro let you normalize on the timeline and avoid a trip to the audio editor entirely. However, normalization is applied equally over the entire audio file, not selectively where the adjustments are needed. If the applause levels at the end of the ceremony are already at the theoretical 100% level, normalizing the file will have absolutely no impact on the bride's whispers. Inaudible before, inaudible after.
In these instances, you must intelligently normalize by working with the waveform in your audio editor. Specifically, you should apply the normalization filter selectively to lower-volume regions within the peaks of applause, music, or laughter. Another option is to avoid normalization altogether and simply adjust volume directly. Once you normalize within each scene, normalize from scene to scene. The best technique is to export the entire project waveform into your audio editor, where the varying heights of the waveform will identify the scenes that need volume adjustment, which you can perform back in the video editor or in the audio editor. If you adjust in the audio editor, import the final audio file back into your video editor, and mute the original audio track. If you pay attention, synchronization shouldn't be an issue, but check synch in all relevant scenes.
The second problem you've probably encountered is random pops and clicks in the video, perhaps where you clicked on the camera's ND filter or kicked the tripod (discreetly, of course). Sometimes these noises have no identifiable cause, making you wonder if they're karmic payback for dissing the A/V guy in high school. Either way, they're there, like a pimple on the forehead of an otherwise-immaculate bride.
Filters designed to solve this problem vary by software program. My favorite tool is Adobe Audition's Repair Transient filter, though I've had good luck with Sound Forge's Click and Crackle Remover as well. The procedure is generally the same; you zoom into the waveform, drag over the offending noise to select it, and then apply the filter.
Interestingly, what's important here is not what the filter removes, but what it leaves behind. If the filter mutes the audio, producing a flat line waveform that would provoke a frantic "Code 2" at the local hospital, the fix will be just as obvious to the listener as the initial problem. Instead, you want only a partially altered waveform that retains the essence of what's going on in the background but without the pop or crackle, which is what Audition's Remove Transient filter seems to do so well. Whatever tool you use, preview the result visually and by playing the file, and make sure that the cure isn't worse than the disease.
The final problem is pervasive noise in the audio signal. Sometimes it's an air conditioning hum, sometimes the whine of a mismatched microphone and camcorder. This is the province of the "noise reduction" filters available in Soundtrack Pro, Sound Forge, and Audition. Note that these work only on regular, consistent noise and can't remove irregular sounds like traffic or crowd noise.
In all three tools, you start by identifying a region in the waveform that contains just the background noise, often called a "noise print." Then you preview the filter and adjust the controls so that you remove as much noise as possible without distorting the remaining audio. When you apply the filter, the program removes the background noise identified in the noise print from the entire audio file, including regions containing other audio, such as speech and music. This feature is very different from "noise gate" filters that mute audio where it doesn't meet a specified volume threshold, leaving the offending background noise in all other regions in the audio file. (For more information, see Luisa Winters' tutorial on Noise Reduction in Adobe Audition.)
Noise removal filters can be a lifesaver, but don't let them lull you into the "fix it in post" mentality. You never know which types of noise these filters will safely remove and how much distortion they will introduce. Still, sometimes you can't control the situation, and sometimes mistakes just happen. It's nice to know that your audio editor has features that can bail you out.