Public transportation will be your best bet. There's a regular inexpensive train that departs from Schiphol Airport to the main train station in the city center. Roughly 4 Euro. Looks like the Hotel Princess is out toward Vondelpark, so you may have to do a little walking but it's not terrible.
Your best bet is to go to Google Maps, click on 'get directions', type in Amsterdam airport & Hotel Princess click the 'bus' icon and read the detailed directions. almost 8 years ago