Maurice, you have been given some great advice about wonderful sites to use in your search. Add one more to the list; Orbitz.
For our planned trip to France I put in multiple destinations into the auto notice option on Kayak. Instead of just looking for flights for my final destination (Paris), I also searched for direct flights into major hubs in Europe. Kayak kept sending me notices, and I found a cheap/direct flight to Frankfurt. Then I booked a flight on one of the lo cost inter-EU airlines (search with Kayak, Orbitz,etc AND whichbudget.com) to Paris.
Make sure that you search at least three days before and after the days you want to fly...sometimes there are flights so cheap on the days or week that you had not planned, that you cannot afford to pass them up.
Always do like Andrea says, and buy your tickets from the airlines directly!
And lastly, check flying "open jaw". (Fly into one city and return home from another. i.e. fly into Frankfurt, return home from Rome) sometimes the savings are phenominal. Enough to pay for the rental car or trains that you use exploring the region, or for the one way flight that you book on one of the cheap EU airlines.