We usually use come to talk about movement from the listener to the speaker or from the speaker to the listener.
Can you come to my office? I need to show you something.
Shall I come to your place at 8 pm?
We also use come to talk about movement from another place to the place where the speaker or listener is:
Rosie is going to come to you on Friday if that’s okay. (a third person moves to the listener)
A man came to my door last night selling pictures. (another person moved to the speaker)
Come is also used with the meaning of ‘accompanying the speaker or listener to a place’:
Are you coming with us to the beach this afternoon?
A:I’m going for some lunch. Are you coming?
B:Yeah, why not.
We can use come to mean ‘arrive’:
Has the post come yet?
Flavio came about an hour ago but Tom isn’t here yet.
When we talk about an event which happens because someone comes to a particular place, we use come and:
Would you like to come and have dinner with us one day next week?
When we simply express someone’s intention or purpose in coming to a place, we use come to:
He came to apologise, but she wouldn’t speak to him. (it was his intention to apologise)
How come? is used informally to mean ‘why’:
A:How about lunch at 1 pm?
B:Not today, I’m afraid.
A:How come?
B:I’ve got a big meeting this afternoon and I need to prepare for it.