I've had trouble understanding tabs (especially pertaining to my right hand) how does it work?

Answer 1

After you have put the fingers in the right spots, you use your other hand to strum or pick the strings.
If you strum, you can choose to hit all the strings or only the higher sounding ones, (make the stroke hit the strings only when you get to the ones you want to make sound.)
Or make a combination of one long stroke and or or more short ones.

If you pick the strings, you can use any pattern, or no pattern at all.
My teacher made me pick the strings like this, the top line is how he would notate the names of the string, starting with the low E:
E a d g b e

ebegebe ebegebe
or: ebgbe ebgbe
or: gbegbe gbegbe
or: Egbeagbe Egbedgbe

Each set of letters would be one measure of the music, so in most patterns you would repeat the same movement each measure, in some you would use the lower strings just a each second measure, the higher strings all the time.

If you look at players like Dylan, he played patterns like these, but not are regular and strict as my teacher taught me.

If you like a particular style of music, see what kind of strumming or picking the guitarists use. (Often in concert videos they do close-ups of the people playing, in the clips you might get a glimpse.)
Once you have seen it you can work out from what you hear what kind of strumming or picking they use, if not the pattern.

Answer 2

you have six lines, each representing a guitar string. Of the six lines, the line lowest on the line is your low E string (your thickest string), and the top line is your high E string (your thinnest string).

And the numbers on the lines tell you which fret to play on that string