Dave
It depends how familiar you are with chords in general. A quick look through the syllabi for ABRSM jazz and I can't see any 7th chords/arpeggios, but there are some 9ths. However, let's stick with 7ths for now. I hope this doesn't confuse you!
Amanda pointing you to Pete's pages is a good start, but to elucidate a bit. Take G7. It' a chord using G as the root plus the 3rd and 5th notes above it, which forms a G triad: G,B,D. Then the 7th note is added. However it is not F# as you might think if you were thinking that G was the first, tonic, note of a scale. G,B,D,F# is in fact denoted GMajor7. What happens in G7 is that F natural is used. If you are still thinking in GMajor, you can consider the F# as flattened. So G7 is G,B,D,F.
7th chords like that (A7, D7, C7..) are known as dominant 7ths as they are built on the Vth or Dominant note of a scale. Thus G7 is built on the Vth note of C major, the notes in the chord thus being taken from C Major are G,B,D,F (natural). You can think of eg, C7 in the same way: C is the Vth note in F major, so the 1st (root), 3rd, 5th,7th notes are C,E,G,Bb. Dominant 7ths are used a lot in jazz and popular music.
It takes a while to get to understand these and other extended chords, but practice will get you there.
I hope that helps, not hinders!
YC