MY PC uses broadband, I want to use my laptop downstairs, how do I do this wirelessly, through LINKSYS or what?

You will need a Wireless router, Linksys is good.
Then Laptop may have wireless built in or added with a USB adapter, Card or other.

As a rule, I don't like Linksys, but that's my opinion of the company and of the product.

As Strat says, you need a wireless router. You should determine what wireless is available in your laptop. Wireless 802.11/b,g is widely available and Wireless n has come into the picture. Usually if the router or the Laptop supports n, it will support b and g. and if it supports g, it supports g.

Wireless is essentially line of sight, so centrally located is best without large obstructions like brick walls.

Wireless is also slower and less secure.