I agree with mysteryman's advice - if you don't feel confident, probably best to get someone in.
If however you do feel like giving it a go, the steps are these:
1. Shut off water supply to cistern, and flush it
2. Bale out remaining water
3. Underneath the cistern, you'll find a large hexagonal nut that secures the flush pipe - undo it using a large spanner or waterpump pliers
4. You'll then see a further large hexagonal nut which secures the syphon in place. Undo it, and be prepared to catch any remaining water with cloths
5. Inside the cistern, remove the c-link (a short, bent piece of wire that connects the flush handle to the syphon's lift arm)
6. The syphon should now lift out - push the lift arm from the top of the syphon, and it will emerge from the bottom
7. You will then see the diaphragm - a little piece of plastic sheet about 4" x 3" (it will probably be torn, or folded, or otherwise unserviceable)
8. Cut yourself a new piece of plastic to replace it
9. Put it all back together, in reverse order to the above
Good luck if you do decide to have a go!