Some of my biggest problems when it comes to understand spoken english, is when they pronounce the word to, it seems that there are two ways of pronouncing it, depending on if you apply stress or not?
Like one way is to pronounce it the same way you pronounce the word "too".
The other way is like the vowel in the word "not".
Any hints on when I must use one form or the other?
The reason you think you hear "to" with a short "O" (as in "not") is because the speaker is actually completely omitting the vowel all together. He's saying, "I am going t'town" - and you think you are hearing "ta town."
If he were to say, "I'm going to the store" you will hear the proper "to" - simply because it's awkward for the speaker to say anything like "I'm going t'the store." If he were to really run the sentence together, it would be more like "I'm goine t'thtore" - but that is almost like a lisp and you wouldn't pick a short "o" out of that.