I'll contradict @TimCampbell on this -- it's very likely that the outer film layers protected the film toward the core of the spool to some extent. The film will likely show some light striking at the edges and through sprocket holes over its full length, but images from the early frames are likely to be salvageable, especially if you were in "subdued light" when you opened the camera.

If you have a local lab that you go to directly, you could take the camera there and explain the situation; they can open the camera in a dark box, remove the film and put it into a cassette, and then process it for you (assuming it's C-41, or that they handle whatever sort of film it is).

Otherwise, you can do this yourself -- but you'll need a changing bag or a room you can make completely dark (a bathroom with no windows, black masking tape over the door closure, and a towel stuffed into the crack at the bottom works well). Then, by feel, you'll need to unwind the film from the takeup spool, roll it up, and slip it into a black film can (if you have one) or wrap it in several layers of aluminum foil.

Once the film is safely protected from further light exposure, you're ready to send it off for processing. Be sure to clearly mark the foil packet as having unprotected film inside, and to open only in total darkness.

Of course, if you're already processing your own film, you can bypass some of this -- just unload the camera in your darkroom or changing bag and load it directly into a processing tank. Once that's securely closed, the hard part is done.