In German you can choose among seven alternatives to address someone: du, dich, dir, ihr, euch, Sie and Ihnen, in English you say you.
Your choice depends on the answer to a couple of questions:
The objective ones are: *How many Yous are there? What is their grammatical case? *
The subjective questions deal with your (intended) relationship towards the “you”: How well do you now the you? How well do you want to know the you? How well does the you want to know you?
Your addressee will be aware of the connotations of your choice and either accept or correct them.
But that’s not all. We have tremendous regional differences. Rule of thumb: the more to the north you move, the more the “du” will prevail, though you might find interesting amalgams, where a person is called you but is still addressed seemingly formally with Frau or Herr x. The construction is actually not formal at all but it provides the listener with a clue that the relationship is not quite familiar (and not on precisely the same social level in the situation at hand), even though the speakers know each other well.
The choice also depends on the milieu that you visit or are (considered) a part of: students at a university, for example, all use the familiar “du” among each other and towards the doctoral candidates and the PostDocs and everyone else who looks like he won’t have the means to object forcefully or who doesn’t look like the grave is already dug. Excluded are the upper echelon and the older members of the faculty; older – and by that I mean *old *– students, however are called “du”, even though they would never be addressed that informally in other circumstances, removed from the college settings (at least not by anyone with more than marginal manners).
When you meet people in business for the first time, the “Sie” and “Ihnen” is mandatory, and you should never ever say “du” to a secretary, even if you have abandoned the “Sie” with her boss for ages - which happens far more often nowadays than in the past, though more among people of a similar age. If there is a distinct difference in age, the younger one will wait for the older to suggest the “du” in most social situations, unless they are socially far removed from each other. In that case, it’s more polite to continue with the “Sie”.
Under more private circumstances, things can be very easy or so difficult that an ethnologist could dispair.
People of my generation (the thirty-/forty-ish) are usually quick to tell the younger ones to use the “du” and we also tend to be not offended if someone we are not familiar with uses it spontanuously in private or informal situations.
But you can usually tell the social background of the speaker by his or her ability to differentiate the many levels of addressing someone correctly in a given situation.
The female teenage friends of my oldest daughter were readily calling my sister “du”, when she told them to do so, but they were reluctant to address the parents the same way (and they quite often revert to “Sie” when they haven’t seen me for a while and almost always when they ask a favour). The male friends of my son had less trouble to use the “du” with me but were shy towards my wife, and the teenage male friends of my oldest daughter make a point in using the “Sie” while talking to me.
Once the friends are considered adults, the “du” is, of course, an easy alternative and readily used because it shows the willingness of both sides to become familiar and be mutually respectful.