There are a some useful reference books to get started, for example:
The Squadrons of the Royal Air Force and Commonwealth, 1918-1988 by JH Halley (Air-Britain, 1988 ISBN: 0-85130-164-9)
RAF Squadrons: a Comprehensive Record of the Movement and Equipment of all RAF Squadrons and their Antecedents since 1912 by CG Jefford (Airlife, 1988, ISBN: 1-85310-053-6)
To find out about RAF Units currently in service, see http://www.raf.mod.uk/stations/strength.html
The Public Record Office contains useful material for further research, for example:
Operations Record Books (ORBs) over 30 years old, files relating to specific commands of the RAF (e.g. Bomber Command) and a number of combat reports.
The Royal Air Force Museum may also have resources to help you with your research. They have a very useful information sheet on the subject which is available at http://www.rafmuseum.org.uk/IndexHendon.cfm
There may be something relevant to the squadron that you are researching in the IWM's Photograph Archive, Department of Documents or Department of Printed Books.