People in the United States don't always shake hands when they are introduced to one another. However, in a formal or business situation people almost always shake hands.

1.A: Mary, this is Joe's brother David.
B; I'm very glad to meet you.
C: It's a pleasure to meet you.
B: How do you like Texas so far?
C: It's really different from what I expected.
B: Don't worry. You'll get used to it in no time.

2.A: Mrs. Smith, I'd like to introduce a friend of mine, Pierre Dubois.
B: How do you do?
C: Hello.
B: What's your impression of the United States?
C: Well, I can't get over how different the weather is here.
B: Oh, you'll get used to it soon!

3.A: Wendy, I'd like you to meet my brother Sam.
B: Hi.
C: Nice to meet you.
B: What do you think of Dallas?
C: Well, I'm still feeling a little homesick and so many things seem strange to me.
B: You're bound to feel that way at first, I guess.

4.A: Mrs.Hughs, this is Peter Brown.
B: Pleased to meet you.
C: How do you do?
B: I hope you're enjoying your stay here.
C: If it weren't for the climate, I'd like it here very much.
B: It always takes time to get used to a new place.