A: Historically I've told people that mixing is the process of combining tracks to make a song, and mastering is the process of combining songs to make an album. That description is less and less apt though, as most of my clients these days submit individual songs rather than albums.
So I'm forced to resort to a technical description: mastering is the process of applying EQ, compression, and limiting (and other tools, if needed) to get the proper tonal balance, punch/density, and volume from a stereo mixdown.
Or more to the point, I make it sound like a record. \U0001f44d\U0001f3fb
A: Mastering is one of those things that you've really got to put your 10,000 hours in on, to achieve a basic level of competence. I only resorted to figuring it out for myself because the mastering on my first two albums was terrible, and I couldn't stand not understanding the process.
Mastering is less of a dark art now than when I started, but it's still shrouded in mystery. DIY tools like Ozone do more harm than good IMHO, because they encourage people to damage their music in a variety of unnecessary ways. If you're going to resort to multiband stereo widening, harmonic synthesis, or even multiband compression, you'd better have a damn good reason for it. Chances are, there isn't one.
If I were starting off now, I'd first ask myself if this is really what I want to do for a living. Otherwise you're better off establishing a relationship with a pro.
If you're set on learning to master, I'd try to intern at a mastering house and save yourself years of figuring it out on your own, like I did. YouTube has some great tutorials, but you'll be overwhelmed with conflicting advice.
A: Start by picking a DAW.
If you're on Mac, that should probably be Logic Pro X, as it's dirt cheap with the strongest feature set of the bunch. Alternately, if you want to perform or DJ with your laptop, Ableton Live might be a better option.
On Windows, I'd probably lean towards Ableton Live regardless, especially if you're producing electronic music. If you plan to mostly track live instruments, maybe Pro Tools or Cubase would be better, though I never got into PT and haven't used Cubase in a decade.
Next you've got to learn to use it! If you're looking for a more hands-on approach than the manual, there's always YouTube. Or something like MacProVideo if you're willing to pay a little for a higher quality, more structured, set of tutorials.
Once you know how to use your DAW, you need to learn how to actually make music in your chosen genre. For electronic musicians, Dubspot, Vespers, and EDMProd are great resources. Reddit likely has a forum dedicated to your genre of choice, where you can network with other producers.