Use bleach water to help clean and also help with the staining. Let this dry, then spray well with vinegar to kill the mold/mildew spores. There is a chance it may have gotten behind the silicone and stained back there. If it did, you may be better taking up the silicone and applying new. Keep the area dry and spritz with vinegar to prevent the mold/mildew from returning longer.
Jackie, I'm thinking you mean silicone caulk instead of grout? Using a razor blade, start by cutting the edge loose, then pull it out. Clean surface with bleach. Rinse, allow to dry, then re-caulk.