It depends. Are you using a Kindle? If you have a Kindle or another ereader that has built-in 3G you don't need Wi-Fi.
But if you're trying to download a book to your computer then yes you will need an Internet connection of some type. If you already have Internet via an Ethernet cord then you should be fine. But if you're computer is too far away or if you want to use Wi-Fi then yes you will need a wireless router and a wireless adapter installed in your computer.