The Silja terminal can be reached from Stockholm centre using local transport. The distance to the city center is only 2 - 2.5 km. One can choose a bus shuttle between the Silja terminal and City terminal or a subway (the nearest subway station Gärdet is 5 minutes walking distance from the terminal). 

For more information, see: 
http://www.silja.com/english/
http://www.sl.com/international/

In order to plan an early trip, notice that the ship returns to Stockholm on Friday, around 9 AM. The International Airport Arlanda is approximately 40 km outside the city and can be reached by bus shuttle or fast train. 

Useful information: 
http://www.flygbussarna.com/flygbussarna/en/index.html
http://www.arlandaexpress.com/