Arpeggios are simply chords in which the notes are played successively rather than simultaneously. They are built from triads, chords of three notes consisting of a root and the third and fifth above it.
For example, the notes in the C major triad are C, E, and G. Let's work on the major and minor arpeggios for the sharped keys: G, D, A, E, B, and F#.
Though I've included suggested fingerings, feel free to experiment with your own variations. These arpeggios span two octaves, but you should try to add a third once you have mastered them. Once you know them cold, you'll find your fretboard to be a much more comfortable place for your fingers to hang out.