What the band can do is pretty simple. Add drums, add bass, add lead guitar arpeggios or backup melodies, add keys. All of this can be created with just knowledge of the chords and care for the melody.
If you're asking what you can do: Try by starting just learning the melody on the guitar. After you have that, just improvise with the melody and the major scale of the key you're in. After that play the arpeggios to the chords and try to make up little accompaniment passages.
I can go into more detail about the specifics of chords and scales if you have specific questions. You might wanna post the lead sheets to a tune or 2 that you're working on and we can break it down.