You've correctly identified the required
firmware-brcm80211 package. But Debian is stricter about the principles of free software than Ubuntu, and so the firmware is in the "non-free" section of the Debian package repository. This section may not be enabled on your system by default, unless you had the foresight to specifically choose it during installation.
/etc/apt/sources.list, there will be one or more lines like this:
If that file is empty, there can be other repository configuration files in
<repository section keywords> might include just
main by default. You'll want to change it to at least
After that, you should run
apt-get update and then
apt-get install firmware-brcm80211. Then either unload+reload the kernel module of your Wi-Fi interface, or simply reboot.