When do you capitalize mom, dad, mother, and father?

Generally, if you can replace the words mom, dad, mother, and father with the person's name in the sentence, you should capitalize them.

For example:

"What did you say, Mom?"

He wasn't going to tell Mom.

"Of course, Dad."

"It's behind the bed--Dad's bed."

By contrast:

My mother lied.

My father was drunk.

His mom wasn't going to give him another cookie, no matter how much he begged.

Note: the same rule applies for titles (Doc, Sergeant, etc.), and other familial relations (Grandma, Grandpa, etc.).