The absolute best way to appreciate another culture is to learn the language and go live in it for a while.
I recommend using an exchange program. The only drawback is most exchange programs are strictly for young people: high school and college students. If you're still in school, look into the study abroad programs your school has to offer.
If you are already out of school, you'll just have to save up for an extended vacation, I'm afraid. But do learn the language before you travel. It's only polite.