One a unique thing to try in Tibet is the famous yak butter tea. It is also called salted tea. Tibetan people drink it almost all the time. And if you want to have a complete Tibetan experience, you should definitely try it as well. Local people believe the tea gives them strength and health.
Every morning begins with a cup of butter tea. It actually tastes salty, and for a foreigner, it may be hard to drink it all. A few sips will be just great as for the first time. Tibetans also drink sweet tea with milk, mainly during the British tea time. There are lots of tea houses in Tibet, especially in Lhasa.
Some people say they have learned to drink tea from British, others say that it was the influence of Indians or the Nepalese, but Tibetans definitely make tea in their own way. And the best way to find out is just to try it!