Up-votes to @stoneyb and @oerkelens. Let me just add:
"My teacher told me that "the" is used before well-known to both speakers objects and if a noun is used for the first time we shoud use "a"."
The first part of that -- use "the" when the noun is "well-known" -- is basically correct. Most people would say to use "the" when we are referring to a specific instance. Like in this case, the speaker is waiting for a specific train, not just any train.
But the second part -- when used for the first time always use "a" -- is just wrong. There is no such rule.
"The Earth has a population of about 7 billion." Everyone knows which Earth I'm talking about, as there's only one.
"The president of the country gave a speech." It's likely clear from context which country I'm talking about, and any given country probably has only one president. So it's "the", not "a president gave a speech". In context, if I was talking about not just the current president but also about past presidents, I might say, "a president once gave a speech in which he said ...", etc. But if I'm talking about many presidents, then it is not necessarily clear which one I'm talking about at any given moment.
"The wife of the murdered man identified the body." If we said, "A wife of the murdered man ...", that would imply that he has more than one wife, which he probably doesn't.
Etc. There are many cases where the first time that a person or object is mentioned, we would use "the", because we are referring to one specific instance and not one of many.