The Russian vowel "o" is pronounced like an "a" when unstressed in a word. You need to know where the stress falls in a word to pronounce "o" correctly. For example, "окно" has the stress on the final "o". The initial "o" is pronounced like an "a". Most Russian textbooks explain these vowel sound changes so refer to your textbook for a full explanation.

In Russian there is a rule: when you don't know which letter must be written, you need to find a verification word. This word has to be with similar root of the word and letter which you need to check, must be under the accent. In your situation verification word can be "говор" (transl: speech). The accent is on the first "o" - "гОвор" and we can't say "гАвор", that is why we can't write "гАворить". Word "говорить" you can pronunce as you wish, but write only "говорить". But it is just one of a lot of rules :)

However, if you learn Russian by ear, there is no way to tell the difference until you are good enough. Then you can read textbooks that explain how to spell the laguage you learned in spoken form. And you will be able to guess the spelling by finding a related word which has a stress where you need, so it is obvious which of the two vowels is spelt there.

That depends on how you learn Russian. Russian kids check the vowels by using a related word, like "разговОр". If you have a Russian textbook, and learn from there, you won't have to guess the spelling: just write the words as in the dictionary.