You have a couple options.
The cheapest is to run a Ethernet (LAN) cable from the router to the computer. This may not always be possible depending on the location of your router.
If your router does support wireless connections (you didn't specify if it's a wireless router or not) then you can buy a PCI card that acts as a wireless networking device, or a USB adapter that does the same. The PCI card is probably more reliable, though you need to know how to open a computer and install hardware and install drivers to the system.
Edit: You didn't specify if you even had the router installed. Without the router you can only have an internet connection on one PC, two if you bridge the connection to the other. With a router, it acts as a gateway sharing the internet connection with all computers networked together.
If you don't have a network set up at all, then you'll need to set up a home network for all the computers you want to connect to the internet with.
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