If you’ve compiled the kernel with the correct drivers and enabled the general ethernet support correctly you should see the following entries when you type
netcfg
in the console:
lo UP 127.0.0.1 255.0.0.0 usb0 UP 0.0.0.0 0.0.0.0 eth0 DOWN 0.0.0.0 0.0.0.0
The usb0 interface is the USB OTG ethernet gadget device (which is by default enabled in the kernel).
Now (do not forget to connect a network cable to your USB ethernet adapter and your router/switch) type the following commands in the console to configure the eth0 interface:
netcfg eth0 dhcp
This triggers the eth0 interface to get the IP etc. via DHCP (of course you need a router with DHCP enabled).
The eth0 interface now should have assigned a valid IP address if everything works like expected.