Depends on the camera's construction. I cleaned the shutter of a Ricoh 500, has been working well. I think three screws had to be removed to take the name ring off, and the front element removed using a rubber cork. Ronsonol (lighter Fluid) did the trick, a couple of applications were required. I checked it last night, and it was working well. I cleaned it about a year ago.
With any old leaflet shutter camera, you might try exercising the shutter at various speeds, starting out on the high-end. Sometimes they work back to life. Otherwise, pop the front and try the Ronsonol trick. Or send it in for a CLA to Essex camera or other shop.