On this B&H video Rob Rives looks at two important tools for sound in Premiere that can help you improve the sound on your videos.
Two of the most basic tools for improving sound levels for professional videos are normalizing and compressing. Normalizing makes sure that a constant amount of gain is added the audio to bring the average or peak amplitude to a target level. If you have a video where some parts are very laud and other parts are very low you might also benefit from compressing.
When compressing sound we are basically reducing the dynamic range between the loudest and quietest parts of an audio signal. This is done by boosting the quieter signals and attenuating the louder signals.
On this video Rives gives some tips on how to normalize in Premire (although it might be very similar in other software as well) and how to specifically configure the compressor for best results.
A few years ago Rives published a complete guide to audio for DSLR which you might also want to check out here.
On LensVid we have a very extensive section devoted to sound recording for video productions which covers both equipment and techniques here on LensVid.
Iddo Genuth 
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