Airfare is usually the most expensive part of a trip, and it’s also where a lot of people seem to have the most trouble finding good deals. I like to use ITA Software’s Matrix — it’s actually the search engine that powers virtually the entirety of the airfare search industry, which means you get behind the scenes information. The Matrix isn’t a booking agent, though, so you will have to go direct to the carriers once you’ve found the flights you want. The extra step means you avoid extra commission fees, and I always like booking directly with the carrier in case something happens on the road — it’s easier dealing with the company directly. The Matrix is also a great place to start researching various options for flights, as it has a bunch of extra options for finding the best deal if you have a flexible travel schedule.
Now, it doesn’t cover all of those European low cost options, so you’ll still have to poke around on your own for that. One site that always helps me planning travel in Europe is eDreams. You can plug in the cities you want to go to and it will tell you what airlines fly there, as well as also giving you an estimate on price. It covers the usual names, like RyanAir and EasyJet, but also some you might not be aware of, like Transavia and Vueling.