Connect an Ethernet cord to the port on the back of your computer as shown. Connect the other end of the ethernet cord to your router or modem depending on what you are using. If you were not provided with a router or modem, you could be on a fiber connection which has slightly different connection instructions.
Your computer should automatically establish a connection. If it doesn't, try restarting your computer.
Tutorial: If you're still having trouble connecting to the Internet check your LAN settings.