Norway's internet network is fast and reliable. Wi-fi, 3G and frequently 4G are available right across the country, often in surprisingly remote locations.
A decent wi-fi connection is widely available at most hotels, cafes, restaurants and tourist offices; it's nearly always free, although you'll usually have to ask for the password or register to use it. Most of Norway's airports offer free wi-fi; the standard service can be slow, but there's sometimes an option to pay for faster access.
Several airlines, including budget carrier Norwegian (www.norwegian.no), have also started to offer free onboard wi-fi for its customers, as has the state railway NSB (www.nsb.no) and some bus services.
Public Libraries & Tourist Offices
Free internet access is available in most municipal libraries (biblioteket). As it's a popular service, you may have to reserve a time slot earlier in the day; in busier places, you may be restricted to a half-hour slot. Be aware that some libraries are replacing their internet-access computer terminals with free wi-fi.
In addition to offering wi-fi, sometimes tourist offices in major towns have an internet terminal as well (for which there's usually a small fee).