No question, Tibet is my favorite destination. Especially the remote high plateau of western Tibet is in its kind simply unique on this planet. Besides the classical route there are endless opportunities to explore new regions.
Since April 2008 it has become impossible to enter Tibet individually. That is when mainly the checkpoint have been reinforced with army personal. Because of that it is no more possible to enter without permit as it used to be for many years. This applies for the whole of the TAR. Outside of it (Kham, Amdo) it is still no problem to travel.
To be allowed to travel in Tibet, you first need a chineese visa like in the rest of China. You best get that at home already. Die conditions change constantly, also how much you will get. Often flight details and hotel bookings are requested. Always check the current situation first. More then 30 days you won't get anymore these days.
One of the best places to get a China Visa is still Hongkong. You will not get 6 month anymore like it used to be, but at least it is fast and without conditions.
There are plenty of agencies that can organise the visa. One of the better one is:
FTB: RM 916-917,NEW MANDARIN PLAZA TOWER B,14 SCIENCE MUSEUM RD, TST EAST, KOWLOON HK.
Usually it is possible to extend a visa twice for 30 days. In theory you can do that with every PSB. But of course there are huge differences, places where that works well, others that are impossible. Some goes here: check the current situation.
Alien Travel Permit ATP
For most places in Tibet you officially need an Alien Travel Permit (ATP) to be allowed to travel. You only get that as a group, with a travel agency. Because of that it is no longer possible to travel independent across Tibet.
Outside of the TAR (Kham, Amdo also known as East Tibet) you don't need such a permit and it is still possible to travel independently. Close to the border there are of course always places that are restricted temporary.
Finding good maps for Tibet is quite difficult. The main maps of Nelles, Gizi Map, Reise Know How are all more or less the same. The best paper map for me is the map from Gecko Maps.
Nowadays I would of course use a GPS and paper maps only use as a backup/for planning. OSM maps are good and cover most roads.
In Tibet you are often far away from the nearest doctor. You should be equipped with a good first-aid kit. I am no doctor but below are some issues that are special in Tibet because of its extreme location.
Most of the tibetian plateau lies between 4000 and 5000m. Everyone can be affected by acute mountain sickness (AMS) regardless of your condition and previous experience! The best prevention is a good acclimatisation. This is best done if you reach the plateau slowly under your own steam (cycling). Above 3500m it is recommended not to climb more than 500m a day (important is where you sleep). So take plenty of time while you climb to the plateau for the first time. Once you are there, your body will adapt to the new situation and the risk to get AMS is much lower. It is important to drink a lot at this altitude. Your body looses a lot of water you don't notice because of the extremely dry air.
I would take Diamox with me just in case, but don't use it as a prevention to get quicker to high altitudes!
It is essential to have a good sun blocker with you. UV radiation is very intense at this altitude. I use one with sun protection factor 50.
Giardia is very common in the himalayas. Water is often contaminated with it. I would filter every water you drink, no matter how nice the stream looks like. Symptoms include loss of appetite, lethargy, explosive diarrhea, loose or watery stool, stomach cramps, upset stomach, bloating, and flatulence. They typically reappear cyclically. A very efficient antibiotic is Tinidazole or Metronidazole. It is not available 'at home' but very common in central asia and Nepal. In China you can also get it in drug stores. Print the picture to successfully obtain it, s the english name is not known.
Mostly the weather is quite good and temperatures during daytime are comfortable. But if teh weather gets bad the temperatures can quickly drop considerably. Good protection mainly for your feet, hands and face are very important.
The 'dog-situation' depends very much where you go to. In the west I met only few dogs and did not often have problems with them. In eastern Tibet though I got often attacked by aggressiv dogs. Some of them have rabies. Whether you want to have a vaccination is up to you.