How to act in this situation: Korean culture and language?

I'm sure they would appreciate your attempt to address them in their language rather than be offended. And that's right, you would say, "Annyong haseyo". Keep in mind that the Korean pronunciation runs the words together so it sounds more like, "Annya-seyo", with the "ng" only very slightly pronounced. I don't know what you're referring to when you say, "Tie tzee na soy yo"... but if you want to say something more, you can continue, "Cho-um pwepgessumnida", which is a formal way of saying, "Nice to meet you". This isn't necessary, but it would probably impress them that you made the effort. The most important thing is to bow respectfully when you say "Annyong haseyo". If they initiate a handshake (it's rude to initiate one yourself), when you give them your hand, don't apply any pressure and allow them to shake your hand. Bow slightly as they shake your hand, while holding your other hand under the arm that's doing the shaking as if you were supporting it. I know it's all very complicated, but that's formal greeting etiquette in Korea! Good luck!