1. Consider the timing of the pieces. It's harder to move from a piece that's in one time (say 4/4) to a piece in another time (say 3/4.) It can be done, but takes more effort.

If I were doing it, I would enter a few bars of each song into my music program, which happens to be Noteworthy Composer, and play along with my computer until I had it down.

2. Are the pieces in the same key? If not, then you modulate. How is that done? You play some extra chords between the pieces, either block chords or arpeggios ending with (memorize this phrase)

the five-seven chord of the new piece.

What does that mean? Suppose the new piece is in G. The #5 note of the G scale is D. (GABCD) So take a D chord and "seven" it, i.e. play a D7 chord. Then start your new tune.

Since folk tunes offer a lot of variety (modal tunes, strange tunes), this might not work every time, but it will usually work.