No, we don't. The vast majority of native English speakers have no idea how to interpret phonemic transcriptions. These symbols are mainly used by linguists, language teachers and other language professionals. They aren't understood by the general public. So how do native speakers find out how to say words? By listening to other people, mainly. If it's a really difficult word, we might ask someone else how to say it. The BBC are an unofficially recognised authority on pronunciation, particularly of words of foreign origin. So, if a BBC newsreader pronounces a word in a certain way, you can be fairly sure that it's right.

I totally agree with Su.Ki., but would add that the British are one of the peoples in the world who care most about pronunciation and accents. Here is an article on how the Queen has changed the way she speaks over time. Yes, people actually research into the way she speaks. It is a controversial matter. While some applaud the fact that she seems to sound more democratic, others deplore the "deterioration".

I don't know IPA. In the United States, it is much as Su.Ki. says. Mostly we just listen. If someone corrects our pronunciation, we usually believe them. Rarely, we will check a dictionary. Typically this happens only when people get into a friendly argument about the correct pronunciation of a word. Ordinary English dictionaries use a simplified system of diacritical marks, and on each page there is a little legend that gives an example of each character-with-mark and a model word that uses it. So, I might look up "aunt," see that the most frequent pronunciation is "ănt", check the guide and see that "ă" is the sound of "a" in "păt," and that's that. In real life, dictionaries are used by people who work professionally with words. People in broadcasting jobs would probably have and use pronunciation guides compiled by the organization they work for.