Greeting when meeting for the first time

Hi./Hello  

In Korea, whether it is morning, afternoon, or evening, you can great people simply by saying 안녕하세요? (an yeong ha se yo?) However, if you are in a business meeting or giving a public speech, you can use 안녕하십니까?(an yeong ha sim ni gga?) instead.
It provides a more formal tone as required in those circumstances and it is mainly used by men in Korea. In most cases, women prefer to use 안녕하세요? (an yeong ha se yo?) 

Nice to meet you.(lit. I am meeting you for first time.)

When you meet someone at first, you can say 처음 뵙겠습니다(cheo um bab get sseum ni da) to emphasize the fact that you have not met previously. If you are in a business meeting, you should use this greeting and then introduce yourself by presenting your business name card. When introducing yourself by name in a formal manner, you should say your full name first and add (이)라고 합니다.((i) ra go ham ni da)

I hope we get along well together.(lit. I will be in your debt.)

After you introduce yourself, you can say 잘 부탁드립니다(jal bu tak d rim ni da) with a slight bow. This is often used in business or personal relationships with others so they use this expression when they first meet someone to show their hopes for a good and productive relationship.The literal meaning may sound as if the speaker is asking for a special favor, but in real life it is simply an expression customarily used when introducing oneself in formal manner.

Pleased to meet you.

Similarly to the above expression 잘 부탁드립니다, 반갑습니다(ban gab sseum ni da) is an expression customarily used after introducing oneself. Compared to 잘 부탁드립니다, it sounds more friendly and less formal, so a bow is unnecessary. You can use this expression in casual and formal meetings alike. In practice it is often accompanied by a hand shake.

What is your name?(honorific)

When you want to ask someone for their name, it is often better to use 성함(sung ham)(an honorific word for 이름, name) than 이름(i rm). You can use this word politely by asking 성함이 어떻게 되세요?(sung hami eo ddeo ke due se yo?) instead. However, if the other person is much older than you or is of higher status, you should always use 성함이 어떻게 되세요?