Mold produces harmful spores so before you begin the task of removing it, make sure you are wearing the appropriate protective clothing, including a respirator. Its also important to find out what is causing mold to grow in your home. Remember, mold does not develop without moisture, so it is likely you have some type of leak or other water related problem that is causing it. This problem must be addressed, or the mold will just continue to grow back.
You can clean mold from hard surfaces using detergent and water. If you will be repainting the area, make sure it is well scrubbed and thoroughly dry before doing so, otherwise paint can start to peel. You should not consider caulking an area where mold is present either.
Soft furnishings are tricky when it comes to mold removal as the stains left behind are not easy to remove. If you want to keep any soft furnishing items, you might want to consult with a professional furniture restoration company. Carpets are another tricky area and it is very difficult to remove mold them. In most cases it is best to replace moldy carpeting.
So then, although it is generally OK to clean up small areas of mold yourself, its important to take the necessary precautions. It is also a good idea to seek the advice of mold remediation specialists to make sure it is safe for you to get rid of it yourself.