Depends what type of light fitting you are putting up.
You may need to find a part of the ceiling where there is a joist and fit screws into the wood. Joist are normally set at specific distances apart. If you can establish which way they run and how far they are apart you should be able to establish potential fixing points.
If it's an upstairs ceiling have a look in the loft for position of joists
To find position of joists you may need to drill ceiling with a very small drill bit (watch out for electric cables.)
To make good damaged area
There's some great products for this job try
Polyfilla One Fill
Very easy to use even upsidedown on a ceiling, wont sag and clean up with water.
Maurice, October 2010