Assuming material is rehearsed and ready to perform, recording is the first step, strangely enough, in the recording process. Though there is a tendency to use technology to correct many flaws, care taken at the recording stage makes subsequent steps much easier. Careful microphone placement, strong signal levels without clipping and controlled noise are some of the details attended to while recording, not to mention capturing a compelling performance. Concentrate on clean, natural sounds. Sweetening happens at later stages.
Digital recording makes editing a breeze. Even the simplest freeware recording programs have the ability to view and edit your audio as a waveform. Removing unwanted breath sounds in a vocal, or bad notes in a guitar solo, become easy tasks. Deleting sections of tracks where no performance occurs can help reduce overall background noise levels. Automation can be used as non-destructive editing to automatically mute sections for arrangement purposes, which are simple to reverse if you change your mind later.
Mixing is possibly the most creative part of the recording process. The raw material of the recorded tracks is shaped and tweaked with equalization, plug-in effects and other digital manipulations. It is at the mixing step that the care you took with the original recording pays dividends -- so you can spend time mixing, instead of "fixing" -- but there are many techniques to help the errors that inevitably make it through. Keeping up-to-date on mixing tricks is a non-stop process, even for professionals.
True mastering requires controlled listening spaces and expensive equipment for commercial releases. In the home studio world, it can be considered processing done on the mixed song. This might be compression or other dynamics processing, and many mastering plug-ins are available to put the final sparkle on your masterpiece. Mastering for the digital realm may require changes to the song's sample rate and resolution for burning to CD or conversion to MP3 or other online music sharing format.