Mobile-phone coverage is generally good, even in far-western Tibet and at Everest Base Camp!
Public telephones can be found in small shops but are increasingly hard to find.
Most hotels in Lhasa have International Direct Dial (IDD) telephones but levy a hefty surcharge on calls.
WhatsApp is blocked in China unless you have a VPN, though Skype seems to work. Most Chinese and Tibetans use the messaging app WeChat.
Buy an inexpensive local pay-as-you-go SIM or data card for cheap local calls, but get it before arriving in Tibet. Buying a mobile phone in China is cheap and easy.
Buying a SIM card
Purchasing a local phone or data SIM card in Lhasa can be complicated, as you normally need to show a local residency card. It's much easier to buy your SIM card elsewhere in China (Chéngdū is a good option) and in fact many hostels sell them at reception.
A SIM card from China Telecom or China Unicom costs ¥120, which gives you around 200 minutes of local calls plus enough data for two weeks of emails and internet usage for most. You can add credit with a credit-charging card (充值卡; chōngzhí ǩa) for ¥50 or ¥100 of credit. It's best to take your guide with you to purchase a card as there are many options.