If this cistern is a UK or european type ROCA or similar, there will be a small plastic float, accessable through an aperture, which may require screwing down (or sliding down) depending on fixture type, to reduce the water level. If the float at its full lift, is submerged and still overflows it may be that the valve seat has been contaminated with debris (if you have had plumbing work done recently) and may need the seat clearing of said debris or the valve seat may be split. The latter 2 options can only be assessed with water off and the valve dismantled. Temporary fixes are possible if it is the valve but it would be better to get a valve rubber from your local DIY store or plumbers merchant. They only cost pence but if you get a plumber to do the work you could well pay heavily. Hope this is of help.
Max Richards, August 2006