Answering a private phone

British people usually give their name or number.
Hello. Susan Fernandez.

Asking for a person

To ask for a person you can say 'Could I speak to...? Americans usually say Could I speak with...?
Could I speak to Jane? (US Could I speak with Jane?)

Saying who you are
Hello, this is Jane. (Not usually I am Jane.)
Could I speak to Alice, please?

If it is Alice on the other side, she will say 'Speaking.' Or 'This is Alice.' In American English it is also possible to say 'This is she/he.'

Asking who somebody is
To know who is answering the call you may ask any of the following.

Hello. Who is that? (US Who is this?)
Who am I speaking to?
Who is that speaking?

If somebody is not there
You can use an expression with 'I am afraid' to say that somebody is not there. To take a message say 'Can I take a message?' OR 'Would you like to leave a message?'

Hello. Susan Fernandez.
Hello. This is Jane. Could I speak to Alice, please?
I am afraid she is not in at the moment. Can I take a message?

If you want to leave a message say 'Can I leave a message?' If you want to ask the person to ring you back you can say 'Could you ask her/him to call/ring me back?' OR 'Could you just tell her Jane called?'

Asking people to wait
You can use any of the following expressions.

Just a moment.
Hold the line, please.
Hold on a moment.
Hang on. (Informal)

Wrong numbers

I think you have got the wrong number.
I am sorry. I have got the wrong number.

Bad Connection
If it is bad line, you may want to hang up and try again later. You can use the following expressions.

Could you speak louder? It is a bad line.
Americans will say It is a bad connection.
It is a very bad connection. I will hang up and call again.