Q:

How are computers that share the same IP address being identified?

The computers in my office share the same IP address. Having that in mind, how does the Internet know that when I request a file from a remote server, it is exactly my computer that should receive the file and not one of the other computers (in my office) that share the same IP address?

A:

It uses the tuple (source ip, source port, dest port, dest ip).
Therefore it does not identify a computer but a connection and that is all that matters from an Internet-server point of view.
You router then has a table that allows him to know to which computer he needs to forward the connection. This is called NAT.

