Greeting refers to welcoming someone with certain words/phrases or a specific action. When we meet someone for the first time we greet by shaking hands and saying "How do you do?" or "Pleased to meet you." or "Nice to meet" or "Nice to see you" or "Nice to have you on the phone" (through phone)
Generally with people we know well, We greet by just saying 'hi' or 'hello'
Here are some expressions you can use to greet and respond people in English:
Greeting [Hi, hello.] Responding [Hi, hello.]
Greeting [Good morning, good afternoon, good evening.]
Responding [Good morning, good afternoon, good evening.]
How are you doing?
How are you doing today?
How are you going?
I'm fine thank you (thanks)!/ I'm doing good (thanx)!/ Thank you (thanks)/Not bad.
Additional: How about you?/And you?
Greeting: [How do you do?] Responding: [How do you do?]
"How do you do?" isn't actually a question, it simply means "Hello".