Hi Rosalie: Good question. This depends on what your ceiling is made of.
If its simple drywall (drywall) the fix is fairly straightforward. If you take the flange out of the ceiling (it may be anchored from above in the attic), you should have a hole that has been 'boxed-in' from above or will simply be between two ceiling joists on 24" centers. The simplist way to fix the hole is to put a piece of drywall that is the same thickness as the existing ceiling drywall but a little bigger than the hole, up into the hole and then rest it back down so it covers the hole, then mark it around the hole opening with a pencil. Then cut a piece of 1/2" plywood so it too fits into the hole so that when you set it down on the opening from above, it laps over the edges of the opening by at least 2-3" or so around the inside of the opening. Then secure the plywood in place by running 1 1/4" drywall screws around the outside of the hole and into the plywood. Then put the piece of drywall you cut into the opening, screwing it into the plywood backer already in place. Then with a sharp utility knife, cut a 'V' grove about 1 1/2" wide where the ceiling meets the new piece of drywall you just installed. Put drywall compound into this groove, then put fiberglas mesh tape into the grove over the drywall compound, let dry, then put another course of drywall compound, let dry, sand and put a final coat of drywall compound, finish sand (flat with the ceiling), prime and paint. If you take your time and do a good job, you will probably have a hard time recognizing your big patch :-)