It's pretty self explanatory, the first person says something to go with the story that rhymes and the next person continues with a rhyme. If you can't think of a rhyme just continue the story and people will try to rhyme with yours. Example:
Person 1: On the well, Billy sat
Person 2: With his best friend, Pete the cat
I will start:
Jimmy was a handsome lad
Person 1: On the well, Billy sat
Person 2: With his best friend, Pete the cat
I will start:
Jimmy was a handsome lad