I understand that fingerstyle guitar is something that is very opinion based (some artists love to accentuate the bass line of the song, while others prefer to highlight the melody)
How does one go about doing it?
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@Slim's answer is great. A couple of things to add.
After you learn some rolls (picking patterns), you'll be able to arpeggiate chords and play chord melody solos.
Now learn to play the melody fingerstyle, concentrating on your picking hand.
First learn to play the melody and/or bassline with just your thumb and index finger. Rev. Gary Davis was an expert at this. Then add the remaining fingers on your picking hand to play chords while you play the melody with your thumb and forefinger. Now you're playing the guitar like a piano--it sounds much less "guitaristic".
Finish off by learning to play the single-note melody line with all of your picking fingers.
By mixing all of these techniques, you will have a rich palette to paint your musical pictures with.
This is very broad, but I think I can break down some introductory steps:
Trying out tabs of other people's songs -- or trying to copy them without the aid of a tab -- or trying to transcribe a tab yourself -- will teach you a lot of this. When following a tab, don't just play the notes without thinking how they relate to chord shapes and scales.