It refers to a person who has deceived or been purposely mean to someone without them knowing/behind their back.
Taken from the coronation street story line that started in 2002 and cultimated in 2003, where Gail Platt was deceived by Richard Hillman.
"Omg did you see Sarah's boyfriend cheating on her with Roxanne?!"
"Yeah, someone should totally tell her that he's doing a richard on her!"
"Please tell me the truth, i know that you have been totally doing a richard on me!"
"Did you hear the things that Jills supposed best friend Mary has been saying about her?"
"Yeah shes so mean! Poor Jill, she has no idea that Mary is doing a richard on her!"