Understanding basic Japanese expressions

For the most part "hai" corresponds with "yes" and is used to express approval and agreement and ideas in a positive sense. Common usages include...
"Hai, so_desu" = "Yes, that's right" or "Yes, it is"
"Hai, wakari-mashita" = "Okay, I understand" or "Right, I see"
"Hai, do_zo" = "Yes, please go ahead" or "Yes, please have some"
"Hai?" = "Yes?" or "What is it?" or "What did you say?"
"Hai!" = "Yes!" (in answer to your name being called)

"Iie" is not used in Japanese as much as "no" is in English because negativity is usually expressed through a negative verb conjugation rather that flatly saying "no". Common usages include...
"(Iie), chigai-masu" = "No, that's not right" or "No, it isn't"
"(Iie), kamai-masen" = "No, I don't mind"
"(Iie), suki ja-arimasen" = "No, I don't like it"
"(Iie), kekko_ desu" = "No thank you"
"Iie!" = "Not at all!" (to a compliment) or "Don't mention it!" (see below)

If you visit Japan, everyone will be thanking you for one thing or another, be it for visiting a store or for riding on a train. Speaking ATMs are bound to thank you as well! Here are some common usages and their rough English approximations...
"Do_mo" = "Thanks"
"Do_mo arigato_" or "Arigato_" = "Thank you"
"Arigato_ gozai-masu" = "Thank you very much"
"Arigato_ gozai-mashita" = "Thank you very much" (for something done previously)

This is quite a formal expression and is not used as much as its English counterparts. In Japan you are not obliged to say "Do_ itashi-mashite" every time someone says "Arigato_ gozai-masu" to you. Other alternatives include...
"Hai!" = "That's okay!"
"Iie!" = "Don't mention it!" (also as above)
"Kochira koso" = "No, thank YOU"