If you arrive at Münster Airport: there are regular buses to the centre (to the Hauptbahnhof). From there you can get a taxi. You can also take a taxi directly from the airport to your accommodation.
If you arrive at another airport: take a train to Münster. At Münster station get a taxi or a bus.
If you arrive by train: take a taxi from the station. A journey from the station to addresses in the city centre will cost about € 12 – 20. You can of course take a bus instead.