Bluegrass banjo, like most banjo music, is dependent on different "rolls" that are performed with the picking hand. The basic "forward-reverse" roll involves using three fingers, your index, middle and thumb. Don't fret any notes when you are first practicing rolls. Start by picking the middle G string with your thumb, then the B string with your index finger and the higher-pitched D string with your middle finger. This is the forward portion of the roll, and it can be topped by picking the high (and shorter) G string with the thumb. Start the reverse portion of the roll by picking the high D, followed by the B and then the middle G string. Use your middle finger to finish with a pick of the high D string. Practice this roll until you are comfortable with it.
The banjo's standard tuning can be technically referred to as "open G" tuning. This means that if you strum all of the strings at the same time, with nothing fretted, you can play a G chord. Lay your index finger across the four, full-length strings at the second fret to play an A chord. As a result of the banjo being in an "open" tuning, moving this basic pattern (index finger covering the D, G, B and D strings on the same fret) up and down the neck of the banjo plays different major chords. (See Resources for a full banjo chord chart.) Ninth, 11th, 13th, diminished and augmented chords are rare in bluegrass music, so you don't have to learn these.
Bluegrass music commonly employs the pentatonic and Mixolydian scales, which you should learn if you wish to play in this style. Scales are sets of notes that sound nice together and produce a certain sound. Generally, the notes within a scale are numbered 1 to 7, starting with the root (or first) note and moving up sequentially (C is the first, D is the second and so on in that fashion). The pentatonic scale is made up of the first, second, third, fifth and sixth notes of the standard major scale. The Mixolydian scale has a flattened seventh, meaning that in C, the seventh, B, would become B flat. (See Resources for a banjo scales page.)
Bluegrass banjo music is full of legato techniques, which are used as part of "licks." Licks can be defined as short flurries of notes played on the instrument. Slides are used frequently in bluegrass and produce a smooth transition sound between two notes. Fret one note and pluck the string. Keep your fretting finger pressed down on the string, but slide it up or down to a higher or lower fret. Hammer-ons and pull-offs are other "legato" (literally meaning "smooth") techniques. A hammer-on is played by fretting and playing a note, then pressing down a higher fret on the same string with another finger while the first note rings out. The note changes as your second finger goes down. A pull-off is the opposite of this.