British people usually give their number or name when answering a private call.

Hello. Susan Fernandez.
Hello. Ardington five three oh double four. (=53044)

In American English, the following pattern is more common.

Hello. Packard residence. John Packard speaking.

Asking for a person

To ask for a person you can use any of the following expressions:
Could I speak to Jane Mathews? OR Could I speak with Jane Mathews?

Saying who you are
Hello, this is Alice. (NOT Usually … I’m Alice.)
Could I speak to Alice?

If it is Alice on the line, she will say:

Speaking or This is Alice speaking.

In US English, it is common to say:

This is she.

Asking who somebody is

To ask who somebody is you may use any of the following expressions:

Who is that?

In US English, it is more common to say:

Who is this? OR Who’s there?

Other common expressions are:

Who am I speaking to?
Who is that speaking?

Asking for a number

What is the dialling code for Paris? (GB)
What is the area code for Paris? (US)

If somebody is not there

If somebody is not there you may use the following expressions:

I’m afraid he is not in at the moment.
I’m afraid she has gone out.

If you want to leave a message, you may say:

Can I leave a message?

If you want to ask the caller if he/she would like to leave a message, you may say:

Can I take a message?

Other common expressions are:

I will ring again later. (GB)
I will call again later. (US and GB)
Could you ask him to call/ring me back?

If you got the wrong number:

I think you have got the wrong number.
I’m sorry, I have got the wrong number.