Disinfecting moldy drywall will work fine for small areas. For larger areas, you will need to consider removing the drywall. For related information, see the articles 'Is Black Mold Dangerous' and 'Removing Mold From Drywall'.
Dealing With Mold Concerns
Is it advisable to try to remove mold yourself. That is your decision to make. Bleach will kill mold and remove it from many surfaces. Precautions need to be taken so that the mold is not breathed in. It also needs to be disposed of properly.
Check out this government website before you mess with mold. A Brief Guide to Mold, Moisture, and Your Home, it will give you some insight and safety tips. Another good article is Mold, on the CDC website. The EPA states that repairs of less than ten square feet can be performed by a homeowner, as long as they follow the guidelines.
Mold Removing Solutions
There are commercially manufactured mold disinfectants available. An example is the 'Moldex' website. They have multiple products that can kill and remove mold. Read the information and determine the product that best fits your needs.
Your home supply store should have a selection. A solution of a quarter to half cup of bleach to a gallon of water will also work.
Cleaning a Moldy Area
Were a mask and disinfect the area. Wipe down the area until the mold is gone.
Discard the rags after you are done and get rid of the dirty water. Let the area dry and make sure that the mold is gone. Use a good quality stain blocker/sealer such as Kilz or Zinnser as a primer. Paint the area as needed.
Drywall mold removal is a repair that should be made sooner than later. Address the problem at the first sign of mold. A musty smell is also an indicator of mold, even if you don't see it.