Tibet is a colossal pain since China seriously restricts Westerners in the region. This may have changed (I gather the level of restriction fluctuates) and I personally haven't been since I didn't want to sign on for a tour.
If you're interested in Tibetan culture but not keen to visit China there are parts of Tibet's cultural sphere that lie outside of China, with some still being on the Tibetan plateau. Ladakh in Indian Kashmir and Spiti in Himachal Pradesh, India, are both such examples and relatively easy to get to.
There's also a large Tibetan community in Dharmsala (also Himachal) where the Dalai Lama is in exile.
I know some Scandinavian countries have an odd ban from Tibet, but Germans are fine to go.
When would you want to go? Going early in the year is not good. They close it to all foreigners for an undetermined amount of time usually from Jan or Feb to either March or April.
You will need to hire a tour operator to obtain your Tibetan permit. DM me and I can recommend what would definitely be the cheapest option. If you are not on a budget, a quick Google search reveals tonnes of options. If you just go to Lhasa, you need a guide to take inside the temples and palaces. Exploring the city on your own otherwise is fine and that is what I did when not going inside of the sites. You can book your own hotel, eat at the restaurants by yourself, walk the town, and even ride the public transportation. Going outside of Lhasa to the typical sites will absolutely require a guide.
Will also need to know where you will be coming from. If you want to go to Tibet direct from Nepal, you need a Group Visa from the Chinese embassy of Kathmandu. If coming from anywhere else you will need to obtain a Chinese visa in advance.
You can read about HERE on my blog, though I am a USA citizen - it may be helpful information.