Most hotels and hostels have free wi-fi, and some hotels have computers and printers in the lobby or business centre.
Wi-fi access at coffee shops is nearly universal and usually free; ask for the password when you order. At bus and train stations and airports, you often have to sign up for an account (usually free) to access the wi-fi.
Nearly all public libraries offer free use of computers, but often the half-hour or hour slots are fully booked in advance by locals. Many tourist offices offer a computer terminal for visitor use (usually free or for a minimal fee). Internet cafes are rarely found in Sweden.