First of all, it helps to have a basic knowledge of music and rhythm to ad-lib, and/or improvise. Ad-libbing is, basically, “playing around with the tune”, using licks, riffs and scales (and/or whatever comes to mind) usually in a dramatic or emotional part of a song.
How Music Is Constructed: Some Basic Music Theory
This is a brief introduction to help you understand the basics of music theory and how that relates to singing and performing a song.