How do you use ruefully in a sentence?

It depends on which type you use. One way you can use it if you think someone will regret something, you could say, "You will rue this day!"

Ruefully is an adverb, so it describes the way someone states something, or looks while saying it. He ruefully apologized for his gaffe.
She looked at him ruefully and replied "That happened over a month ago! Can you please forget about it."