Removing moldy drywall is the best choice for larger infected areas. Or if the paper on the drywall has been ruined and/or the core of the drywall has started to disintegrate. You will need to remove and replace the drywall.
For drywall with mold on it, make sure you dispose of it in tightly sealed plastic bags. Take safety precautions, wear gloves and a mask when you are around moldy drywall.
See the government website for information on the issues, A Brief Guide to Mold, Moisture, and Your Home provides some good information. Disinfect the entire area after the bad drywall is removed. See the article 'Disinfecting Moldy Drywall' for more information.
For drywall that has been compromised by the water damage and mold you will need to replace it. For instructions on removing and replacing drywall go to the article 'Replacing Larger Areas of Drywall', for a discussion on the steps involved. This is a bigger project so brace yourself.