There are 2 computers located in the cafeteria area on the 1st floor. For the cost of 350 IKR you can get 30 minutes and for 600 ISK you can get an hour on the internet. If you don't use up all your time, the code you get is valid for 24 hours from the first time you activate it.
You can also print out from those computers, in black and white, where one A4-sized page costs 50 IKR.
There are wireless networks in the library. Anyone with a laptop and a wireless network connection should be able to log on to the internet, free of charge.