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 To Feel Rhythm
Feeling Rhythm is imperative for any singer
For Classically Trained Singers: A Few Tips On How To Sing Modern Genre Songs
The modern genre is very different from classical styles