"Wildwood Flower" was a folk standard long before it was made famous by the Carter Family. It requires only two chords, E and B, to play, and anyone can learn to play it on guitar with a bit of practice.
Playing Wildwood Flower on guitar
Play an E chord. Leave the top, or E, string open. On the second and third, or A and D, strings, cover the second fret with your middle and ring fingers. Use your first finger to depress the first fret on the fourth, or G, string, and leave the remaining strings, B and E, open.
Play the B chord. Bar all the strings on the first fret with your pointer finger. Depress the third fret of the A and D string with your ring and pinkie fingers. On the D string, depress the second fret with your middle finger.
Play the song. The strumming pattern you should follow is up-down-up-down in a steady motion. Here is what the first line of the song should look like:
E chord------------E chord------------B chord---------E chord Oh I'll twine with my mingles and waving black hair
Once you can play with the simple strumming pattern, change the speed and pattern as you like. Play along with the song at first to get down exactly when the chord changes are.
Some people have trouble holding bar chords: Let gravity do as much work and possible, and try to use the side of your pointer finger when barring, not the direct pads, because the creases in your fingers may prevent the barring. Practice is the best method to get bar chords down.