A while ago, I took one of those really cheap C-media usb audio adapter and to make it work, I had to do the following on Raspbian.
Add the following lines (this line will load a linux kernel module called 'snd_usb_audio' that will enable kernel to auto-load audio device drivers over usb ports).
netto@bella:~$ sudo nano /etc/modules
# c-media headset
snd_usb_audio
netto@bella:~$ sudo nano /etc/modprobe.d/alsa-base.conf
options snd-usb-audio index=0