I'll look it up

At a pay phone

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Operator: You don't know Frankie Stone's number?
Boy: No, could you give me her number, please?
Operator: Her number is listed in telephone directory.
Boy: Oh, the phone book, hold on, I'll look it up.
Operator: Please hang up.
Boy: Hang what up?
Operator: Hang up the telephone and then look the number up in the book.
Boy: But I can't find the book.
Operator: There is a telephone directory in every pay phone.

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1- What does "I'll look it up" mean?

Does it mean "I'll find it"?

2- What does "look the number up in the book" mean?

Does it mean "search the number in the book"?

Thank you