There is no TRUE, KNOWN cure for dropsy, if it is indeed dropsy. There are things that people swear by, but, if it is dropsy, and you're going to try to cure him, you're going to have to move fast.
First, what do you have on hand?
Some people recommend using epsom salt baths. I don't know absolutely for sure what the dosage on that should be, but have been told that maybe it should 1 tbsp for 5 gallons, same as aquarium salt.
Some people swear by colloidal silver as a cureall for every possible ailment...if you can find it. I think it's wuvmybetta that uses the stuff.
Some sites recommend immediately getting the Betta on antibiotics like Tetracycline.
Whatever you do, clean water is a must. Sterilize everything, and let nothing you use (including your hands) come into contact with any of your other fish at this point. May not be contagious, but there is no point in risking it.
I wish you the best of luck, and I hope the little guy pulls through.
I'm offering you two links to Bettas with dropsy posts from the past, in hopes that the advice offered there will help you now.
http
/www.fishforums.net/index.php?showtopic=85647
http
/www.fishforums.net/index.php?showtopic=85705