There is two way to connect router to the computer.
Establishing an Ethernet Network
Network adapters already built mostly in computer. You can look on the back side of your computer you have a network port. Network ports look like a telephone jacks, but they have eight pins, and they are a little bigger. If your computer does not have a network port, you can buy a network adapter from electronics retailer.
A coaxial cable connected on back side of modem and one ethernet cable connected computer to the router, plus one ethernet cable to connect the router to the cable modem.
Start your computer and log on. your computer automatically detects that you are connected to the Internet.
Establishing a Wireless Network
Today most of computer connected by wifi with internet.
Start your computer and log on. You should be open your web browser, and log in to your router to configure it to work with your computer. the router has an IP address that you access from your computer using your web browser, such as Internet Explorer or safari.
How do I Connect My Router to My Computer?