There are different ways to greet people:

Greeting means welcoming someone with particular words or a particular action.
When meeting people formally for the first time, we greet by shaking hands and saying "How do you do?" or "Pleased to meet you."
"How do you do?" isn't really a question, it just means "Hello".
When young people meet informally they sometimes greet and say "Give me five!" and slap their hands together (high five).
Generally we do not greet by shaking hands with people we know well. We greet by just saying 'hi' or 'hello'
Here are some expressions you can use to greet people.

Greeting

• Hi, hello.
• Good morning, good afternoon, good evening.
• How are you?
• How are you doing?
• How do you do?

Responding to greeting

• Hi, hello.
• Good morning/Good afternoon/Good evening.
• I'm fine thank you (thanks)/Okey! Thank you (thanks)/Can't complain/Not bad.
• How about you?/And you?
• How do you do?

Things to remember about greeting:

When you greet someone and say:

"How do you do?"

this isn't really a question, it just means "Hello".