If the device you are using to connect to internet is a modem and in it's documentation it does not specify that it has a router or that 2 or more computers can be connected to it at the same time, then you need to buy a:
option 1) router, a wired one. You will have to set it up (it's very simple)
option 2) network card. For this option to work you have to set up ICS on the computer in which you place the second network card.
Have you used the wireless connection of the laptop before? I don't get this part from what you said.
