If you arrive to Bratislava Milan Rastislav Stefanik Airport it is an easy thing to get to the city center. There are taxies standing outside the airport which will take you to the city center, but they have various prices and charge you more than if you simply call for a taxi as you arrive to the airport. If you order a taxi using phone the rate is normally around 15 Euro. If you use the taxis standing outside the airport the rate is normally 20 Euro or more.
You can also use public transportation. Bus 61 will take you to the main train station, and from there you can easily get around in the center of Bratislava. You need to buy a single ticket valid for 60 minutes to do this ride.