I have a desktop internet connection and I recently purchased a laptop. Can I use my desktop connection also with my laptop? If so, how?

It depends on your Internet link. If it is a call-in connection you require a dial-in card.
If you have ADSL you need a network card. If you want to use both computer and laptop simultaneously you need than a router to share the connection
Often dial-in and network cards are integrated in the laptop. Check the operation manual, and get the required cable(s).

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