I realized this morning that the Fedora link would not be helpful except to add to your knowledge of the topic.
Ubuntu has the required files available if you can get to a wired connection. In the Synaptic Package manager, go to Settings-->Repositories and enable the "Proprietary Drivers . . ." item, then hit the "Seach" button and search for Broadcom or BCM. There should be similar settings in the Ubuntu Software Center, but I don't know where to find them. I prefer Synaptic or apt for package management.
I think the package you want is "Broadcom 802.11 Linux STA wireless driver source."
Files are also available from Broadcom, but it will be easier if you use a wired connection, even if you borrow one from a friend for a few minutes, and let Synaptic do the installing.