Probably through research, and the will to become a part of his forgotten Klingon heritage. If you hear him speak Klignonese, you will note that it has an accent not seen among other Klingons on Star Trek, so he probably decided to start following the Klingon lifestyle, and did some research on their traditions and rules, to "become" one.probably by studying them or visiting the homeworld but it should be noted that he didn't live his entire life on earth and that he was around six years when his family was killed.
His adoptive parents taught him about his heritage and even took him to Qon'os for a visit once.
Umm . . . Ebooks? Holosuites?
They kept making a big deal out of it
Given how Klingons actually act Worf learning about Klingons through books etc makes a lot of sense. Worf clings to the Klingon ideal like few actual genuine Klingons do