Hi there, welcome to LQ.
First thing to do usually is figure out exactly which Broadcom device it is. After that, we can figure out where the driver is and how to install it (if it is not installed already). Most of the time, Ubuntu has a way or means that's pretty straight-forward for getting most software, but drivers can be an exception sometimes.
Since you haven't told us what methods you HAVE tried as yet, maybe the following will be familiar to you, and if so, please tell us:
From the terminal, post the results of the following:
If possible, do not post the WHOLE long list of stuff that the command generates -- just locate the block of text that reads "Broadcom blah blah blah wireless device" and post that block of text for us.
Getting ahead of myself:
From what I've read, you will need the STA driver from broadcom, located here:
And also from what I can tell, this driver is not available from your Ubuntu software repository (if I'm wrong, this is good! That would be simpler.)
So, assuming this is indeed the driver you need, go ahead and download the proper version from that link -- either 64bit or 32bit depending which architecture you are running. Download the README file too. Read the README, and attempt to follow the instructions, which are basically:
1) extract the driver source-code from the compressed archive you just downloaded (this means, decompress the archive).
2) enter the newly created folder, which was created when you extracted the archive, and open a terminal.
3) execute the MAKE and MAKE INSTALL commands, as described in the README file (or perhaps other included file that has the instructions.)
Do not worry if these instructions are Greek to you -- post for us the output of the command `lspci` as given above, download that driver, and let us know where you're at as far as extracting the driver and following the instructions that came with it. We'll continue from there.