In Standard Russian, only the stressed "o" is pronounced as an open "o" [ɔ] (you should, actually, pronounce a very short "u" in front of it but I doubt you can show a full IPA description here). If the "o" is situated in the syllable before the stressed syllable or if the "o" is directly at the beginning of a word but in a unstressed position, then it turns into a short "a" [ʌ]. In all other positions, it turns into a schwa-like sound [ə].

ПА-русски гАвАрят не толькА мАсквичи.

Если буква "о" стоит под ударением, то она произносится как "о". Например: дом, кошка, цветок. В остальных случаях - можно произносить как "а".

When it is not accented. There is only ever one "o" in a word which is accented (unless there is a e with umlaut - this will always take precendence - and the accent). The question is how do I know which "o" is accented? As in Домодедово? I am afraid you will just have to join the rest of is in learning these one by one ........... Good luck!

Don't forget that Russia is a rather big country. That means that there are slight reagional accents here. Besides, people of many nationalities live here, not only Russians. In some areas (for example, in national republics) there are fewer Russians than people, whos mother tongue is not Russian. It means that their and Russians' pronunciation are influenced very much by other languages. Anyway, even if you pronounce words as they are written, you would be understood. If you want to become perfect, I would recommend you to listen to old audio recordings. You can find some of them here: http://audio.arjlover.net/audio/ (tales for kids) or http://radioteatr.arjlover.net/