Mold cannot grow without the presence of water. This means that there may be an underlying issue such as a water leak that you will need to diagnose and treat first, otherwise, the mold problem will keep recurring.
You can remove mold from hard surfaces with detergent and water. Scrub the area thoroughly and make sure the area is completely dry before you apply any paint, if not, the paint could start to peel. Do not apply caulk to a moldy surface either.
There are some areas where mold and mildew are very difficult to get rid of, carpeting is one of those areas. If a carpet in your home has mold, it is better to replace it. When mold forms on soft furnishings such as curtains and cushions, it is extremely difficult to remove the stains it leaves behind. If you desire to keep them, it would be best to seek advice from a furniture restoration company.
Before you start the mold cleanup process, make sure you have the proper protective clothing and wear a respirator to prevent inhaling mold spores. Keep other household members away from the area unless they are wearing protective gear also.