Tibet (Tibetan: Bod, Chinese: 西藏 Xīzàng) is an autonomous region of China.
There are seven prefectures in the Tibet Autonomous Region:
Almost all Tibetans speak or understand some Mandarin Chinese. In the cities people speak Chinese fluently; in the villages it may not be understood at all. Chinese is also the language of the police. Han Chinese people, on the other hand, normally don't know any Tibetan at all.
Although this makes Chinese a more useful language for travelers in many ways, you should remember that language is political in this charged environment. If you speak in Chinese to Tibetans you are associating yourself with the Chinese government, which is resented by many Tibetans. That said, many Tibetans seem to view Chinese as a useful lingua franca and a few Tibetan pleasantries is enough to befriend Tibetans. If you speak Tibetan to Chinese police you'll raise suspicions that you may be in Tibet to suport Tibetan Independence. Try to avoid letting police (even ethnicly Tibetan officers) know you speak any Tibetan.
You can fly to Lhasa but flying in from a much lower altitude city puts you at high risk of altitude sickness because of the quick transition. If you are in Sichuan Province or around (and aren't satisfied visiting the many easily accessible ethniclly Tibetan areas to the east of the Tibetan Autonomous Region) flying from Chengdu is the easiest option.
There are four roads into Tibet, roughly corresponding to the cardinal directions:
North: The road from Golmud (Ch:Ge'ermu) is the easiest legal land route at present. It is however nearly as costly as flying, if one follows all the rules, i.e. travels by bus. The landscape is beautiful but difficult to appreciate after the long rough ride.
It's possible to travel this way by hitch-hiking on trucks if you are well prepared (camping equipment, food and water for a day). Expect to spend a few days. There are police checkpoints on the way but the only one that is a problem is the one 30 or so km out of Golmud. If you walk around it and a few km beyond you should be able to get a ride without too much of a problem. There are plenty of places to eat on the way but be prepared to get stuck in the middle of nowhere. There are also are places to sleep ranging from truck stop brothels to comfortable hotels, however these should be avoided as you're likely to get picked up by the police.
East: There is no legal way to travel this road and the security is tighter than from the north. Travellers do get through this way, but for people who are obviously not Chinese it's dificult.
West: From Kashgar (Ch:Kashi) much of the way is technically off limits. However there is a steady stream of hardy travelers coming this way, usually hitching rides on trucks. The road is totally unpaved for over a thousand kilometers with villages and water few and far between. The main advantages of this way is that it passes by Mount Kailash and through a beautiful, very remote region inhabited by nomads. You should be very well prepared to travel this way and take everything you would need for independent trekking: camping equipment suitable for freezing temperatures even in summer, a good tent and at least a few days of food (there are a few truck-stop places on the way but not always when you want them). Expect the trip to take two weeks or more. From Kashgar it's much farther to go to Lhasa via Urumchi and Golmud but the better transport (trains and good paved highways) make it no more time consuming to travel this way. There are many interesting things for the tourist to see on the way and it is worth considering traveling this way instead of via Mount Kailash.
South: From Nepal the international border makes any sort of breaking of the rules impossible, so the only option is to book a tour with a travel agent in Kathmandu. If you have a Chinese visa before getting to Nepal, you will probably be able to stay in Tibet after the visa expires, if you get the visa in Kathmandu it will probablly be only be for the duration of the tour.
Many parts of Tibet are technically off limits to foreign tourists without travel permits. Exactly where you are allowed to go and where not, is a matter of great dabate among travellers. It is complicated by the fact that the police don't seem very clear about it themselves and as you normally get the permit through a travel agent they have a tendency to overstate the need. The truth seems to be that you don't need one for Lhasa Prefecture, you do for all others, and permits can be acquired in the prefecture capital or in Lhasa. The term "prefecture" is being used to refer to the administrative level one down from state. The police in each prefecture seem to hold discretionary powers to a large degree. In Lhasa they do not give permits to travelers directly, only through a travel agent and only once a tour has been booked. In other words it's expensive in Lhasa. In Xigatse the police are happy to give travel permits to tourists directly for a small fee, but they can only issue them for their prefecture, which includes the road to Nepal. Ali is another prefecture where the police give out the permit without any unneccesary difficulties, their administration includes Mount Kailash.
Central Tibet has an OK public bus network, although the strict need for a travel permit when taking a bus (the driver/conductor will want to see it) limits the usefulness of buses.
Jeep tours are a popular way of getting around Tibet, while not cheap, the tour operator will sort out all the necessary paperwork, and they offer you a reasonable chance of sticking to a schedule.
Hitchhiking can be an good way to get around the country for someone who is flexible and has a lot of time. It can, however, mean you end up getting stuck without a lift for days. In the west of the country this probably means hanging around truck stops, as the distances are far too long to walk, and finding water would be a major problem. In central and eastern Tibet, there's more water and villages, and so walking becomes a more reasonable option. In short, hitching may or may not get you to your destination any quicker, but at least it offers a change of scenery.
There are a surprising number of tourists traveling Tibet by bicycle, both foreigners and Chinese. The roads vary from rough dirt tracks to good quality paved roads. There are restaurants, truck stops and shops scattered around often enough so that you don't need to cary more than a day's worth of food (with the important exception of the west of the country). The roads are often well graded, being built for overloaded trucks. 26 inch wheels would be prefrable as 700c are almost unknown in China. Good mountain bikes are avalable in large cities of China or in Lhasa. Golmud is not a good place to get a bicycle (assuming you want it to get you past the check point 30km outside of town).
Good road maps of Tibet are common in China, but only in Chinese. These are of limited use even for people literate in Chinese as the Chinese names are very different from the ones used by the Tibetans. They are useful for reading road signs, even for people with low literacy in Chinese.
The Star publications map is probably the best. Amnye Machen Institute publishes an excellent map of similar scale and detail but with the Tibetan names, with a version written in Latin script and one in the Tibetan. It makes a useful companion. Tibetmap.com has a free downloadable set of maps covering much of Tibet with detail almost good enough to use for independent trekking.
Tragic as the Chinese takeover may be, many Tibetans will nevertheless admit that at least it brought some decent restaurants. Even good Tibetan food is very monotonous with most Tibetan restaurants serving nothing other than thukpa (noodle soup) and tea. Even Chinese restaurants in villages often put out some excellent food. Some travelers feel that Hui (ethnic Chinese Moslem) places are cleaner because of halal food laws; they can be recognised by the green flags and crescent moons (and because they do look cleaner).
While traveling be prepared for the bus to depart late or break down. Carry a snack on short trips and enough food for a few days or a week or more for longer journeys, such as to Mount Kailash. Instant noodles are convenient even if you don't have a camp stove. They can be eaten cold or softened with boiled water. Tsampa (roasted barley flour) is an ideal travel food because it's already cooked. Eat it mixed with tea, butter and salt, or as a high energy snack by mixing it with water, milk powder and sugar.
Tea houses are an important social venue in Tibet, and offer a chance to sit down and relax. The tea houses in the larger town and cities offer sweet tea, or salted; in the villages you may only have the option of salt tea. The line between a tea house and a restraunt is blurred and many also offer thukpa.
When traveling in the countryside be prepared for the vehicle to break down and for bad weather. Carry a snack and some warm clothes.
Be aware of the dogs. In the cities there are numerous stray dogs about and in the country side the villagers and nomads keep large guard dogs (usually chained up). A modest level of caution is enough to prevent you from being bitten, as the strays are normally more afraid of you than you of them. If guard dogs are unchained, keep them at bay by staying away from the house or tent they are protecting and pick up (or pretend to pick up) some stones. Much is made of the viciousness of the Tibetan dogs, but few travelers have problems with them.
Stay away from political protests and keep up to date on political developments. Tibet info network (www.tibetinfonet.net) is a good source of up to date new from inside Tibet. It's usually blocked in China but you can get around this by signing up for email news letters before going to China.
Generally speaking, it is easier getting out of Tibet than in.
It's easy to get travel permits in Xigatse and once you have one you are free to travel to Nepal by any form of transport you like.