The open source b43-fwcutter drivers can be used with these cards, but often give sub-optimal performance (high cpu usage, for example). This alternate setup has given excellent results on the Broadcom bcm4312 and should also work on other cards in that family.
Run the following line in terminal:
sudo apt-get purge b43-fwcutter && sudo apt-get install linux-headers-$(uname -r) broadcom-sta-source
Reboot and you should be good to go.
Note The above method requires an active internet connection! So find a cable and plug in.
Here's a copy/paste from a post by forum member maguffin
Jockey-gtk is a graphical tool to detect and install proprietary drivers for certain hardware. Before you can use it though, you will need to roll back your kernel to a version that is known to work with the Broadcom card. One kernel that has worked is 2.6.38-7-generic. The PAE version also works with machines that have more than 4G of RAM.
Open Synaptic via Applications > Preferences > Synaptic Package Manager. Hit Reload. Search on 2.6.38-7-generic. If you want to try other kernels, do a search on “Linux-image” and you will see a variety of options . Mark the Linux Image for installation and hit Apply.
You will now see another Bodhi Linux option in Grub listing the 2.6.38-7 kernel version. Boot into that option.
Download the linux headers for the kernel you booted into by entering the following in a terminal:
sudo apt-get install linux-headers-$(uname -r)
You can download Jockey-gtk via the Bodhi Software Center or by typing in a terminal:
sudo apt-get install jockey-gtk
Launch the program using sudo from the terminal. It won't work if you launch it as a regular user:
You will see the Broadcom driver listed as an option. Click on that and hit Activate at the bottom.
The indicator should turn green. Reboot back into the new kernel and after a few moments, your wireless card should be detected and available wireless networks listed.