If you look for cheap flights from outside of Europe to Slovakia, use one of the comparison sites for flight ticket prices. Some of them search in databases of all airlines flying from your location to Slovakia and you can easily compare which flight is the cheapest. However, if you look for flight inside Europe, it is better to look for flight tickets of low cost airlines like Ryan Air or EasyJet.
Here you find cheap flights to Bratislava.
Slovak Airlines Video
Slovak Airlines's Boeing 737-300 lands in Bratislava.