What do I do with an aggressive dog???

I agree with spiritdogs, positive training.  Follow the NILIF techniques and establish leadership. 
 
My dog and I both loved obdience training (although he was over a year and knew all his basic obdience) it was fun, he was star (being oldest) and the socialization was wonderful.

She's beautiful!  I love the darker Chessies!

strong corrections applied to aggressive dogs tend to make them more aggressive.

I wholeheartedly agree with this.  My lab, Sassy, has dog/dog aggression and also a propensity to react aggresively to harsh corrections.  I learned early on that using those types of corrections became a "battle" of wills and I wasn't going to win.  After visiting with a behaviorist and her confirming that we needed to use only positive corrections, I found that Sassy was quite eager to please if given the chance.

I would never, ever consider putting her down either, but I can see where outsiders who aren't dog lovers might consider the risk too great and suggest it.  I know some people thought we were crazy for keeping Sassy and managing her and our other dog separately.  It takes constant vigilance here at home and in public places, but knowing what I'm dealing with keeps me prepared at all times.  Sometimes I feel sad that I can't sit in the waiting room at the vet and let Sassy give nose kisses to the other dogs in there, but I accept it and deal with it.