Your BeagleBone Black won't be able to access the Internet with the default network-over-USB configuration, but there are a couple ways that you can connect your BeagleBone to the Internet.
The simplest option is to connect the BeagleBone to your network using an Ethernet cable between your BeagleBone and your router or a network switch. When the BeagleBone Black boots with an Ethernet connection, it will use DHCP to automatically request an IP address and register on your network.
Once you have your BeagleBone registered on your network, you'll be able to log in to your router's interface from your web browser (usually found at http://192.168.1.1 or http://192.168.2.1) and find out the IP address that was assigned to your BeagleBone. Refer to your router's manual for more information. The current BeagleBone Black Debian images are configured to use the hostname beaglebone, so it should be pretty easy to find in your router's client list. If you are using...