Go to http://rpmfusion.org/ and add both the free and the non-free repositories unless the latter one is against your philosophical stance.
You can do this via graphical setup, installing a small rpm file that will set this up for you, or at the command line where you can basically just copy the commands into your terminal (you have to become root for this).
Update your repositories and install all updates prior to proceeding.
Search for broadcom-wl, install the package and reboot.
Voila, there you are. Enter network credentials into NetworkManager or Wicd if you prefer that and you're online. It's never been easier.
And here you can find the respective page on the fedora community website, with links to more wireless solutions.