In fluent speech, the labio-dental fricative /v/ is often dropped in two cases.
First, in the preposition of, normally when this is followed by a word beginning with a consonant, because otherwise it would probably be linked to the following vowel. Remember that of is pronounced /əv/, not with /f/, as Spanish speakers tend to think.
So, after the elision, it sounds just like a single schwa: /ə/. Listen to it in these interesting examples:
There were lots and lots of books written by people interested mainly in spelling reform (David Crystal, BBC4). ǀ ˈlɒts ə ˈbʊks ǀ
I’m quite a precise sort of person (Cambridge Advanced test). ǀ ˈsɔːt ə ˈpɜːsən ǀ
The first letters we have between the two of them (Susan Doran, BBC4).
You’re listening to Word of Mouth on BBC Radio 4 (Michael Rosen, BBC4).
The second case involves the auxiliary verb have and is normally simultaneous with the elision of /h/. So, again we are left with just a schwa: /ə/. Despite being very common, the elision of the /v/ in have is seldom described in books.
Here are very good examples (a warning to sceptics: notice that the first speaker is none other than David Crystal, a very authoritative linguist, speaking about English and pronunciation, to boot. So, if he doesn’t speak properly, who does?).
You can offer new spellings as an indication of how the word might have been pronounced (David Crystal, BBC4). ǀ maɪt ə biːn prəˈnaʊnstǀ
Imagine how difficult that must have been if you were a nine or eleven year old girl (Marion Gibson, BBC4).
So that I think he would have thought of as his major work, certainly, it’s enormously longer, as you know, three large books of discourses on the first ten books of Livy (Quentin Skinner, BBC4).
It seems to have been consciously invented in the late 19th century (Norman Davies, BBC4).
This is the type of work I do with my students in my one-to-one classes. I make them practise these processes with exercises until they improve their comprehension of native speakers and are capable of speaking like that themselves. If you are interested in my classes, you can contact me here.