If you haven’t read the tutorial on fingerpicking pattern #1 yet you should do so before playing this arrangement. The top line, of course, is simply the melody. The bottom tablature line is the accompaniment pattern that you will play. Try this pattern with other songs also. You should experiment with playing this pattern with other songs that you learn also, and then you can decide when you would like to use it in your own playing.
There are several different guitar arrangements of Red River Valley on ezFolk to give you an idea of a few of the various ways you can play it. Here are links to each of them: