You can also play them with the pick instead of your fingers. Look at the LEGEND on the right side for the picking and fingering notations used in the diagrams.
Learning guitar fingerstyle patterns is an excellent way to add new dimension to your playing applying them to the chord progressions. Unlike the strumming patterns, where you hit a number of strings simultaneously, here most of the patterns are played with "string by string method" (similar to arpeggios), this creates more melodic and soft sounding.
The dotted lines in the diagrams represent relative positions of the strings, and the lowest line wouldn't necessarily be the low E string. For example for the open C chord it would be the 5th string, for the open D chord is the 4th string.
Note that you "can't" just put the pattern 2 and 3 let's say on the D open chord because you'd need 5 strings and chord is played using just 4, be flexible to adjust patterns to your situation, you can skip skipping the string before the 2nd note (pattern 3) and move the rest of the notes one string lower.
By the way this new formation sounds better for some songs, so don't be bound by the diagrams, feel free to exchange notes, alternate bass note from one string to the next on each second bar and so on...
In this finger style pattern the thumb alternately switch between two bass strings.
Pattern 16 - Traditional Waltz
Pay attention that waltz has 3/4 time signature, it means that duration of 1 bar is equal 3 quarter notes, and not 4 as with 4/4.