There are several terminals at Arlanda Airport. Terminals 2 and 5 are used for international flights. Terminals 3 and 4 for domestic flights. To find out which terminal your airline is using, consult this list.
Arlanda Airport is located 35 km south of Uppsala. To get from and to the airport there are trains and buses. The trains leave from Arlanda Central station located below Sky City between terminals 4 and 5 (see the map above). The buses leave from bus stop number 13 outside terminal 2, 4 or 5 (the bus stops are numbered the same way at all terminals).
Tickets to the Uppland Public Transport trains (a.k.a. Upptåget) are sold at the Uppland Public Transport (Upplands Lokaltrafik) counter in Sky City just next to the entrance to Arlanda Central station. The price is SEK 120. At the same location there are also automatic ticket dispensers where you can by tickets using a credit card. Travel time is approximately 18 minutes.
Bus tickets are sold on the buses (cash only) for SEK 100. Prepaid tickets that can be paid also by credit card are sold at the ticket counters in the arrival halls. (Make sure that you buy a ticket to Uppsala.) Travel time is approximately 45 minutes.