I'm am European (French) and plan a holiday in Tibet.
Considering the political circumstances, I assume I need to apply for a visa to stay there for 3 weeks, is this correct?
If yes, what's the procedure at the moment (2015)?
Currently no new permits are being issued for travel before April 1 and all travelers in Tibet at the moment have to exit the country by 15 February.
If you plan to fly in via China, you will need to apply first for a Chinese Visa (standard tourist visa). Then through the tour company arranging your Tibetan travels you apply for a Tibet Travel Permit. If you plan to visit the Everest base camp or other restricted areas, then an additional permit to travel there is required.
For overland travel into Tibet from Yunnan or Sichuan, an additional travel permit is required.
If you plan to enter from Nepal, then you need a Tibet Group Visa in lieu of the China Visa (unless you plan to continue afterwards in China). Plus all of the Tibet permits mentioned above.
The China Visa, Tibet Group Visa and Tibet Travel Permit all need to be arranged before arriving by several weeks. The Everest base camp and overlanding permits are applied for after you get there.
The company arranging your Tibetan travels can handle most of this on your behalf (except the China visa which you apply for at the nearest Chinese Embassy).
Of course, as this is China & Tibet, rules can change without notice and do so frequently.