As a current student at DIS, you are provided with an SL transportation pass, which is valid throughout your summer in all zones of the SL transportation system. Note that transportation to the airport requires an extra charge to your regular pass, if you use the Pendeltåg to get to Arlanda C.
In the metro and the Pendeltåg, card readers are installed at the entrance to the platforms. If you take the bus, you will find the card readers upon entering the bus next to the driver, and for light rail services you board the train and a conductor will come and check the ticket during your journey. If you accidentally leave your SL card at home at any point, you can still use the metro, bus or Pendeltåg by simply bleeping your credit card on the card reader where you would normally bleep your SL card.