The problem is that exposition arrives before the audience wants it. Information given to someone who has no question in mind is noise; the same information given to someone who has been made curious is a reward. Almost every fix for clumsy exposition is a fix of order.
The reliable techniques all work by giving the audience a reason to want the fact. Put it in an argument, so it is being used as a weapon. Put it in a correction, so somebody is wrong first. Withhold it until a scene stops making sense without it. Or cut it and find out whether anybody missed it, which they usually do not.
The version to avoid is the one where two characters tell each other things they both already know. It is instantly recognisable, and it signals to an audience that the piece does not trust them.
How do you avoid clumsy exposition?
Reorder before you rewrite. Give the audience a question before you give them the answer: put the fact inside an argument, a correction, or a moment where the scene stops making sense without it.
How much backstory does an audience need?
Very little. Cut it and see what anybody misses. Most backstory serves the writer’s confidence and does nothing for the audience’s comprehension.