There are two driver choices for Broadcom cards: bcm43xx and NDISwrapper.
bcm43xx is an open source, reverse-engineered driver. It requires firmware from the Windows driver for the card, which is extracted using the fwcutter tool. Most recent distros include it. Use apt-get to install it if not. Read the docs carefully to avoid mistakes.
NDiswrapper uses the entire Windows driver. Use apt-get to install ndiswrapper, if it's not already installed. The Wiki gives instructions on how to install the Windows driver from there.