It may take years of patience to jump the formal barrier between ‘du’ and sie’, but once accomplished, you’ll have a German friend for life.
The formal rules of etiquette are simple. When meeting someone for the first time, address them as ‘sie‘ and continue to do so until the informal ‘du‘ becomes absolutely unavoidable (for example, while sharing the post-coital cigarette and enquiring politely about earth-movements, etc.). A general guideline is that when you move on to first-name terms, ‘du‘ becomes appropriate.
Social context will offer guidance: in business, never deviate from the formal. The Germans will remain on ‘Sie’ terms with colleagues even after decades of sharing an office, and a boss calling his secretary by her first name will be universally suspected of having an affair with her. At radical student functions, informality may be the rule.
A staged transition
German reluctance to move on to the informal level reflects how ernsthaft a matter friendship is. Some Germans accomplish the transition by stages. To begin with, you will of course be addressed as Herr or Frau X. Later, should you discover sporting or other interests in common, and perhaps a mutual acquaintance or two, you may be addressed by your full name: ‘So, Frank/Francine Jenkins, I am very pleased to see you once more…’
Finally, after many months or years, you will move to first-name terms, and ‘du‘ will ensue. A variation on this, which should not cause alarm, is if you are called exclusively by your surname, ‘Ach Jenkins, my old Freund!’ It is essentially the same thing.
From public to private
The strict separation of the public from the private provides a guarantee that in private the Germans are open and sincere. They may lack polite cushioning phrases, seeing them as a waste of language, and keep their distance from strangers and acquaintances much longer than the English, but when you cross the Hellespont of the ‘du‘ it means that all reservations are gone and you have made a friend for life.