First of all, Wi-Fi is not a direct connection to the internet, it is a Wireless LAN technology (LAN = Local Area Network) it only works about 300 feet at most, which should cover the average home.
First thing you're going to need is a high speed internet connection. This can be either DSL from the phone company, or Cable modem from the cable company. This is your internet connection. You'd need to contact one of the two to get set up with a connection.
Next thing you need is a wireless router. The Wireless router allows you to share your high speed internet connection with all the PCs in your home either with an Ethernet cable, or with Wi-Fi. Wireless routers are widely available in stores and online. AT&T does even offer a DSL modem that has a built in wireless router to their DSL customers.
Now the Wi-Fi card in your laptop is usable at other places that offer free Wi-Fi to patrons. Hotels, restaurants, coffee houses, oil change places. Many of these businesses offer free use of Wi-Fi to their customers while they wait.