Wireless routers allow data from the internet to travel through the router's antenna and broadcast through the air to wireless devices using a wireless adapter. Setting up a wireless router involves running setup software, connecting the router to a computer with an Ethernet cable during setup, creating a wireless network name and password, and potentially manually configuring the router if needed. It is important to enable strong encryption like WPA2 on the wireless network for security. Connections can be tested by using the ping command to check communication with the router.