Cheap ticket search engine: This is a search engine only. It will search several sites at once and find the TOTAL cost (including taxes) per ticket for several carriers, then give you a link to those carriers where you can continue booking your ticket or make modifications to your travel plans.
Airlines: These airlines offer both cheap and unreasonable ticket prices around Europe. Check them often and play with dates. From penny flights to flights costing 100Euros, there is quite a disparity depending on time of year, day, departing airport, etc, so you just have to keep searching and be flexible if you can. The ticket prices quoted are for ONE WAY and taxes will be added. Baggage also costs extra. Do read the fine print and be aware of any restrictions. And, remember that the name of the airport can be deceiving. Frankfurt/Hahn isn’t in the middle of Frankfurt and Dusseldorf/Weaze is a treck as well. Look at the map and be prepared. Allow for ample connection times between flights as well.