From time to time, people have asked me how to look for cheap flights. I'm not an expert, but here are my recommendations:
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Skyscanner is the best flight search website existing now (for Europe). You can use the interactive map, or search prices through a whole month or to a specific country. My favourite feature is that it helps you look for flights for weekend breaks from specific place to anywhere possible! It doesn't let you book in its system, but checks live prices and has direct links to the relevant websites.
There are also other flight search websites, most of them targeted to a specific country:
You can also check out directly the airlines websites. Known cheap airlines are:
ryanair | easyjet | wizzair | germanwings | vueling | volareweb | aegeanair
Of course you can always go to your nearest travel agent and let him do all the dirty work for you ;)