I recently installed Linux Mint version 12.10 on my dell mini. I had upgraded the stock hard drive to a ssd and decided to try something new. My hardware all worked fine with a fresh install with the exception of the wireless network adapter. On the Dell mini 10v you probably have (like me) a broadcomm wireless card. It’s very easy to fix and get it working here are the steps.
1) Find out if you have the same wireless card as me. Open a bash shell and run this command
lspci -vnn | grep 14e4
I get this: 09:00.0 Network controller : Broadcom Corporation BCM4312 802.11b/g LP-PHY [14e4:4315] (rev 01)
2) If you see something different, stop and keep looking elsewhere for a solution. Otherwise install the broadcomm driver with this command:
sudo apt-get install firmware-b43-lpphy-installer
3) Now reboot and you should have wireless working.