Arietta is a low cost linux embedded module: http://www.acmesystems.it/arietta I already talked about it, here:
The adapter is based on asix hardware, you can find it in various shapes:
My build enviroment is based on a debian linux, created with vagrant.
There is this very good tutorial on acmesystem website: http://www.acmesystems.it/compile_linux_3_16 on how to compile a new kernel for the board.
Instead of following the tutorial untill the end, when you reach "make ARCH=arm menuconfig"you have to enable the "Multi-purpose USB Networking Framework" and select the appropriate ethernet adapter:
You can find the section under Device Drivers / Network device support / USB Network Adapters.
After you have rebooted with the new kernel you can plug the adapter and see if the device is recognized typing "dmesg".
My ethernet device is recognized as "eth0", in order to configure it with dhcp you have to edit /etc/network/interfaces on arietta and insert these lines at the end:
iface eth0 inet dhcp
Plug the ethernet cable, reboot the board and... done!