Only recently, I became aware of the correct pronunciation of the preposition of (although I did pronounce it correctly most of the time before). Surprisingly, the correct pronunciation does not involve an f! The frequently heard but incorrect pronunciation [ɒf] is only correct for the word off.
According to the Longman Pronunciation Dictionary, the strong form is pronounced as [ɒv] (British) / [ʌv] (US), whereas the weak form is pronounced as [əv]. The informal short form, sometimes written as o’, is pronounced as [ə]. You can listen to the different variants here, and to off here.The dictionary points out that of is a rare (possible the only) example of a word where f is pronounced like v, which does restore my faith in the English language.
The fact that of is pronounced with a v makes it sound almost identical to ‘ve (contracted form of have), which explains the common mistake of writing, for example,
You of improved a lot. (wrong)
You‘ve improved a lot. (right)