Arriving in Arlanda
Preliminaries
Most international flights arrive at Terminal 5. I have never been to any other terminal, so if you're arriving at another terminal, this page will be less useful to you.
In any case, you can get the #801 bus to Uppsala. I believe that it visits all of the terminals at Arlanda. The #801 is a Regiontrafik service of Upplands Lokaltrafik. You can get a timetable by selecting "801" from the Regiontrafiken menu on their website. The timetable changes in mid-August, so there's little point providing a direct link here.
If you arrive at Terminal 5, you get the #801 bus from stop #13, just outside the terminal building. Up to the 17th of August, #801 buses leave Terminal 5 every half hour at 12 and 42 minutes past the hour throughout the day between 04:12 and 01:12, and at 42 minutes past the hour otherwise (i.e. there are no buses at 01:42, 02:42, and 03:42).
The bus costs SEK 100 (~€11.00) one-way. You can pay cash on the bus.
On the city buses in Uppsala, you are strongly discouraged from paying cash: a pre-paid Busskort is much cheaper (half the cash price). This is not the case on the airport bus. It is possible to buy a ticket from a booth in the arrivals hall, but there is no discount for the pre-paid ticket, so there is no reason not to pay cash on the bus.
Detailed Directions
When you come out into the Arrivals Hall in Terminal 5, you are no more than 30m from the bus to Uppsala.
Straight in front of you, you can see a café, which has replaced the information desk shown in the photographs.
Just left of the café (where the Information Desk is in the photographs), there is an exit.
The sign over the door tells you that you can exit here to get the Airport Shuttle (bus).
When you go through the exit, you can see bus-stop #13 where you get the #801 bus to Uppsala.
The final photograph shows the last few people getting on the bus to Uppsala. This photograph is taken from the other side of the road, so you don't actually see the bus or the stop from this angle.
Arriving in Uppsala
The bus takes about 30 minutes to travel to the Bus station in Uppsala.
