The quickest way to get your Raspberry Pi connected is to use an Ethernet patch cable and just plug it into the back of your home network router.
As soon as you plug your Pi in, you should see the network LEDs start to flicker.
For most home networks, you should also be able to connect to the Internet without any further configuration. For this to work, your router should be configured for DHCP (Dynamic Host Configuration Protocol). This service runs on your home network router, dishing out IP addresses to any device that connects to it either through WiFi or by cable.
If DHCP is not turned on, on your home network router, then connect to its management console using a different computer that is already connected.
You should be able to find a setting somewhere that turns it on.