Finding cheap flights to Europe and the Schengen countries in particular is much easier if you have access to the internet. There are websites such as Kayak that search for cheap flights for you, and travel agencies that do likewise. However, not all airlines will allow aggregators to access their flights so in this case it is better to book direct with the airline itself. Prices fluctuate daily so make sure you look for any companies that are having a sale, or track flights using Google Flights and book when the price drops significantly.
Most airlines raise their prices in the two or three weeks before departure to take advantage of last-minute shoppers, but holiday companies like Tui and Thomas Cook do the opposite. Their business plan revolves around package holidays, so last-minute seats will be sold off cheaply in order to fill the plane. For the other airlines it is better to book from around 6 weeks to 12 weeks before departure, as this is when their seats are likely to be cheaper.