You can get rid of the mould by using dilute bleach or a proprietary fungicide - good scrub & dry followed by another scrub and dry - then perhaps decorate.
As for stopping the mould returning you may never stop it completely but there are things you can do to reduce it and possibly stop it coming back.
Dampness causes the mould - the dampness either comes through the wall from a leaking gutter perhaps so check the outside of the house when its raining and remedy any problems - or - the dampness comes from inside and most probably from condenstaion - warm wet air against cool exterior walls.
Reduce the heat in the room as much as reasonable - increase the ventilation as much as possible - keep doors closed to prevent the steam from bathing and cooking wafting around the house. Turn the heating down a bit especially at night and try to leave a window slightly open when someone's sleeping in the bedroom and during the day when its not in use.
If you can get one, a dehumidifier will help a lot. Central heating and double glazing will be playing their part too - with a warmer environment and fewer natural draughts so you need to compensate by providing more ventilation by opening windows even a tiny bit in kitchen, bathroom and bedroom during cooking, bathing and sleeping. Wipe away dampness when you see it
Good luck...
Peccavi
March 2009