The first will be in 4/4 time (march time) and the second will be in 3/4 time (waltz time). You simply play the chords of the tune, but instead of strumming you finger-pick the strings. Some guitarists grow their fingernails in order to do this, or use picks, but these are difficult to use. You may find it easier just to pick with your bare fingers.
For the sake of demonstration, I've chosen the same chord sequence for both styles.