Sound on Mac Mini 3,1 under Lucid Lynx

1) Add repository: ppa:ubuntu-audio-dev/ppa:

sudo add-apt-repository ppa:ubuntu-audio-dev/ppa

Or through menu Software Sources
2) Reload.:

sudo apt-get update

3) Get to know you kernel:

uname -a

4) Install appropriate kernel:

sudo apt-get install linux-alsa-driver-modules-2.6.32-22-generic

(it was in my case I mean 2.6.32-22)
5) reboot

sudo shutdown -r now

if you want to have alsamixer back:

sudo apt-get install alsa-utils