a) "I often dream of becoming an astronaut." - ambition - "of" needed b) "I often dream about becoming an astronaut." - sleep - "about" preferred. c) "I dream of her often" - more literary, romantic sense relating to a person - could be either sleep or ambition or a mixture.

To dream of something implies you have aspirations and hopes. Something like, "I dream of being a teacher one day." To dream about means you actually have a dream, as in you're asleep and you dream about being chased by monsters.