Remove background noise as much as possible (record in a quiet place to make life easier!). Some editors have automatic ways to remove background noise. Generally, automatic options are good enough for me. Sometimes I make adjustments, but I keep reminding myself that it does not need to be perfect.
In Camtasia: Follow this guide.
In Adobe Premiere is more complex, but still user-friendly. For even more control may want to use Adobe Audition, which integrates with Premiere. I only do basic editing, but may try some of the more advanced tips next time.
For a free option, try audacity.
Basic audio editing functions are included in most video editing programs.