Talking with Someone for the First Time

-ㅂ니까? [(p)-ni-kka?] ending makes the sentence more polite.

• Informal version of 'Hello' is 안녕 [an-nyeong].
• Formal version of 'Hello' is 안녕하세요 [an-nyeong-ha-se-yo].
• More formal version of 'Hello' is 안녕하십니까? [an-nyeong-ha-sim-ni-kka].

처음 뵙겠습니다. [cheo-eum boep-get-seum-ni-da]
I think I'm seeing you for the first time. (Greeting)

• 처음 [cheo-eum] means "for the first time"
• 뵙다 [boep-da] is the humble form of 보다 [bo-da] which means 'to see'
• -겠습니다 [-get-seum-ni-da] has a meaning of "I think" or "I feel"

만나서 반갑습니다. [man-na-seo ban-gap-seum-ni-da]
Nice to meet you.

• 만나서 [man-na-seo] means "because we're meeting"
• 반갑습니다 [ban-gap-seum-ni-da] has a meaning of "I'm glad."

• A: 처음 뵙겠습니다.
  I think I'm seeing you for the first time.
• B: 처음 뵙겠습니다. [cheo-eum boep-get-seum-ni-da]
  I think I'm seeing you for the first time.
• A: 만나서 반갑습니다.
  Nice to meet you.
• B: 만나서 반갑습니다. [man-na-seo ban-gap-seum-ni-da]
  Nice to meet you.