If you are from outside of Europe and you need to book a flight ticket to Slovakia, use one of the airfare comparison sites. They search in all airlines databases, so you can easily compare which flight is the cheapest. These are not very good for searching cheap flights in Europe as they usually don't include low cost airlines (like Ryan Air, EasyJet, etc.).
If you need a cheap flight to Slovakia inside Europe, check out the information in the main content of this page.
Air Slovakia Video
Air Slovakia's Boeing 757-200 takes off at Hannover-Langenhagen Airport in Germany.