The pronunciation of this vowel can be daunting at first, but once we learn the rules it is actually no more difficult than learning the pronunciation of a similar vowel in English (think about how in the word 'repellent' we do not say 'rep-ell-ent' but in fact something closer to 'rup-ell-unt'). This process is called vowel reduction.
In Standard Russian, 'o' is only sounds like English 'o' (as in 'not, hot, bot') when it is stressed. In all other position, it is reduced, meaning it sounds more like English 'u' (as in hut, mutt, pun) or 'a' (as in hat, matt, can). For example, let's take four Russian words that have this 'o' pronounced in it's two different ways.
'Што': Here, as there is no other vowel which could be stressed, the 'o' is not reduced, and the pronunciation is 'shto'.
'Шоколад': The final vowel in this word, 'a', carries the stress. This means the first two vowels are reduced, and so the pronunciation is 'shukulád', with the final syllable sounding the loudest.
'Отец': Again, as the stress is on the second syllable, the first 'o' is reduced, making the pronunciation 'atyéts'.
'Очень': Here, the stress is on the first vowel, and so no reduction occurs. Therefore, its pronunciation is 'Óchen'.'
Of course, this relies on knowing where the stress in a word falls, but Russian is often quite predictable in this regard, as as you progress in the language you will notice some patterns develop. It does help however when learning new words, to always note where the stress occurs, as this will allow you to pronounced it correctly from the beginning.

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