There is no one answer to the question. A commenter to a youtube video on this rather important subject notes that in current English, it is pronounced like this or this, not like this (a hilarious mispronunciation). The last time a fellow academic asked me the question, I refrained from telling her the original pronunciation of חבקוק (you have to have a background in comparative Semitics to discuss the matter properly), and limited myself to repeating the traditional Hebrew pronunciation, “hav-a-kook,” with the accent on “kook” (pronounced here). To which she instantly replied, “every family hav-a-kook.”
On a more serious note, a commentary I wrote on Habakkuk for the open access Bible Brief series is now available. You are welcome to download it from this site. The editor of the series is Stephen L. Cook, who blogs at biblische Ausbildung.
For everything you wanted to know about the name of Habakkuk, but were afraid to ask, see John F. Hobbins, “Il nome del profeta Abacuc,” Rivista biblica italiana 35 (1987) 307-311. I wrote that article when I was 8 years old.