Most hotels, cafes and even restaurants now offer free wi-fi access (无线网; wúxiàn wǎng). Sometimes hotels will only offer it in the lobby. Connecting to the internet through a smartphone's 3G or 4G service is often more reliable and coverage is good in central Tibet.
Internet cafes (网吧; wǎngbā) are in almost every town in Tibet, but few allow foreigners to use the computers.
Some social-networking sites (such as Facebook) and websites (eg those of the Dalai Lama, but also Google) as well as apps like WhatsApp have been blacklisted by the Chinese government and are unavailable inside China unless you use a VPN (virtual private network), which is essentially an easy-to-use piece of software for a laptop computer or an app for a smartphone. Make sure you install this before departing for China.
Gmail is also spotty but again usually works well with a VPN.