Ever since it became a #2 single in 1973, "Duelin' Banjos" has been one of the most universally popular bluegrass songs in the repertoire. People like it for the simple, hummable melody---not always a characteristic of bluegrass-banjo music ---the call-and-response interplay between the two instruments, the snatches of "Yankee Doodle," and the fiery breakdown section. Luckily for would-be players, the song is as easy to learn as it is fun to play.
"Duelling Banjos," based on Arthur Smith's 1955 plectrum-banjo/five-string-banjo duet "Fuedin' Banjos," is a banjo/guitar duet where the two instruments play essentially the same lead line, even through the extended breakdown section.
The song is based off of a simple I-IV chord progression -- a G chord and a C chord, in this case -- and consists of two sections: The melody and the breakdown.
The melody includes part of the tune "Yankee Doodle" as well as the first five-eighths of the G-major scale.
Start by listening to the piece or watching performance videos on a video-sharing site like YouTube. See if you can tell where the melody part ends and the breakdown part begins. Pay attention to the "shave and a haircut" break at the very end where the guitar drops out and the banjo plays an unaccompanied lick.
Tune your banjo G/D/G/B/D, top (short string) to bottom. Tune the guitar E/A/D/G/B/E, top to bottom.
The banjo player should have fingerpicks and a thumbpick, while the guitar player should have a flatpick.
The banjo part isn't difficult, but it helps to know the first- and second-fret C and D7 forms as well as the single-finger barre forms five and seven frets up the neck. (The original banjo player, Eric Weissberg, came from a folk rather than a bluegrass tradition, so he stuck to simple patterns -- lucky for you.)
There's a "tune-up" introduction on the original version from the Deliverance soundtrack. Skip it, wait for the guitar to play a G chord followed by a C and a G again, and echo it. When the guitar restates the change, pick it again, and when the guitar introduces the melody echo it, using the second and third strings. Play the strings open and then hammer-on the D7 chord, playing the second and third strings on the first and second frets, respectively. (It sounds far more complex than it really is.) The first "Yankee Doodle" phrase is played the same way, and then it's back to a restatement of the original melody.
There are two ways to play the phrase which follows the "Yankee Doodle" phrase: move up the neck or move up strings. Moving up the neck preserves the undertones and lets you play the same notes on the same strings, only barring with your first finger instead of using the nut as your barre. Think of the first statement of the phrase as the G-major statement. It's followed by a C-major statement and finally a D-major statement, capped off by a strong G-C-G change.
The second time through play a longer version of the "Yankee Doodle" phrase, which leads into the first breakdown segment. There are many ways to play the breakdown, and just about any major-key breakdown and two- or three-finger roll will work for the eight bars of the breakdown. First-finger barres in the C (fifth fret) and D (seventh fret) positions are good platforms for breakdown improvisation.
Once you're through the breakdown the melody section repeats at the faster tempo of the breakdown. This leads to another breakdown segment, another restatement of the melody and a final breakdown. By this time you're ready to end, so use whatever stock ending you have and then conclude with a big, bold G chord. Let the banjo ring; you've earned it.
Good news: The guitar portion of the song can be played entirely in the "cowboy-chord" positions of G, C and D7 spiced with hammer-ons and pull-offs.
Play with a pick, and the biggest acoustic guitar you can find. You'll need it, or you'll be buried by the banjo. Start with a strong G-C-G strum followed by the first statement of the melody, which starts on the D string and features second-fret hammer-ons to the B string. (This can also be played one octave up, starting on the B string third fret and moving up to the E string.) The remainder of the melody falls naturally under the fingers as open-string/hammer-on combinations starting on the D string and working up to the B string, first fret. The ascending/descending pattern the banjo plays as fifth- and seventh-fret barres work best moving up strings. The first (G major) statement starts on the G string and works up to C; the second C major statement starts on the B string, first fret (C) and works up to the E string, first fret (F); the third statement starts on the B string, third fret (D) and works up to the E string, third fret (G). It all ends with a strong G-C-G strum.
In the breakdown sections, play percussive "boom-chik" chords as backing for the banjo, with a moving G-A-B line in the bass leading to the C-chord change, and D-string, second-fret hammer-ons during G-chord sections. Repeat melody-breakdown-melody-breakdown-melody-breakdown.
At the end, drop out for the banjo's "shave-and-a-haircut" mini-break, then hammer the last chord.
The guitar part can also be played by tuning to an open D and capoing, or by tuning to an open G. In those cases the fingering patterns mirror the banjo.