The format is totally dead. You can't buy film or get it processed commercially. (I think there is just one place in Australia charging 20 pounds per disc!)
However it is sometimes possible to pick up expired film on ebay and because the processing is C-41, you can do it at home. You can see my guide to this here.
I've successfully developed film which expired in 1993.
How to develop Disc film
The film is in a cartridge which also contains a shutter or slide to protect the film from light. This shutter is moved in and out of place by the camera when you load the film. The first step is to get the film out of the cartridge.
So in the dark, find for the tapered edge of the cartridge and feel for the corners at the opposite end. If you push these away slightly the cartridge should open easily allowing you to access the film.
Handle it by the plastic hub only and drop it into a standard development tank. The negative film is much thicker than normal 35mm film so it will stand up ok without buckling. If you are developing more than one, you can fix them together using a small cable tie through the hole in the hub, just be careful not to scratch the film.
Then you can seal the tank and develop as normal C-41. Just let the film rattle around and don't bother inverting the tank too much, just swirl it around. After processing you may notice it has a blue finish. this will disappear after a few mins.
With any luck you will have some pictures!
Don't be too concerned if the colour of the disc is not as pretty as a lab processed one from the 80's, it will scan digitally just fine.