Hi Openmind
Have you ever considered changing your moniker to "DoubtingThomas"? 
(Just teasing you a little!)
To put it in the simplest possible terms, using 'of' instead of 'to' when telling time is basically simply a matter of replacing the word 'to' with the word 'of'.
Since of basically follows the same "rules"/pattern as to, I'd say an Ameican ESL teacher is likely to treat this usage of of a bit like an idiom since it is usually covered only after the basic mechanics of time-telling with 'to' have been mastered, and also because this usage is a special characteristic of American English. (By the way, the words til and before are also sometimes used instead of to). As I mentioned, I would not expect this usage to be covered in a beginner level lesson on telling the time. Therefore, by the time an American teacher presents the usage, there is no need to rehash all of the basics of how to tell time in English. If I went into all of the basic details of telling time with students who had already mastered the basics, they'd not only be bored silly, but would probably think I was nuts to boot. On the other hand, if I had a beginner-level group and attempted to teach them 'to', 'of', 'til' and 'before' all at once, they'd only end up totally confused -- and they'd probably think I was nuts, too. 
This usage of 'of' does tend to be a spoken one since people normally use numbers rather than words when writing the time. In other words, in written English you're likely to see 5:45 instead of 'five forty-five' and '(a) quarter to/of/till/before six', or 2:55 instead of 'two fifty-five' and 'five of/to/till/before three'. However, if you read novels (by authors such as Steven King, for example) or spend time talking with lots of Americans, you will be able to see/hear this usage of the word 'of' in action.
Here is a German ESL site that mentions the use of 'of' instead of 'to':
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And here are some more sites to look at:
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