Ok, let's see.. how the hell did I do it in the first place??

)
Firstly, I installed Slackware Linux v12.1 (of course).
1. Then, without editing any files (such as /etc/rc.d/rc.wireless.conf), I
installed the firmware for my WLAN Adapter.
Clicking here will teach you how to install your device-specific firmware. Since I have found it quite difficult (as a REAL NOOB) to install it from there, I will outline the main points and will show exactly what I did to install the firmware:
1a. Download
Fwcutter v011 and place it in a directory. For the sake of this explanation, let's say you will place it in the /root/Fwcutter directory.
1b. Cd into the "
/root/Fwcutter" directory ("cd /root/Fwcutter") -- if you don't have that directory, use '
mkdir /root/Fwcutter' and you will have it

1c. Untar Fwcutter using this command: '
tar xjf b43-fwcutter-011.tar.bz2'
1d. Cd into the new extracted directory: '
cd b43-fwcutter-011'
1e. Install the firmware: '
make'
1f. Exit the directory: '
cd ..'
Voila! Now you have your tool (
Fwcutter) that will enable you to install the firmware needed.
2. Download the
Broadcom's Proprietary Driver (v4.80.53.0). This works, however only on the following Linux Kernels:
Linux-2.6.24, including 2.6.24-rcX and 2.6.24.Y. Check out your Kernel Version using the command '
uname -r'. If you have a different version, download a different driver from
here.
2a. Untar it: '
tar xjf broadcom-wl-4.80.53.0.tar.bz2'. (into a folder like you created for fwcutter)
2b. Cd into the folder: '
cd broadcom-wl-4.80.53.0/kmod'
2c. Then just apply this command: '
sudo ../../b43-fwcutter-011/b43-fwcutter -w /lib/firmware wl_apsta.o'
Voila! Now you have your Broadcom Proprietary Drivers installed. But you've not finished everything. I would recommend issuing a restart to your system - I am not sure it's needed, but I would advise you to.
3. Now you need a WORKING tool to connect to your wireless networks. As advised by Forum 1793, I used
Wicd Manager.
3a. Download the file somewhere on your computer (preferably somewhere where you won't forget where it is, such as
/root/wicd).
3b. Cd into the folder where you can find the downloaded file
3c. Issue the '
pkgtool' command and select its first option. Select the package you have just downloaded and let it install it.
3d. voila once again

I don't think you need to perform any other tasks yet, so just
RESTART YOUR MACHINE ('shutdown -r now')
I don't know if it is going to connect automatically, but after logging in again, just go into X by using '
startx'. There, your Wicd Manager should have appeared in the taskbar or in the KMenu. You can learn using wicd using the 'wicd --help' command, but I would recommend starting x and configuring its graphical interface. There, you should find the wireless networks in range and everything you need will be there.
Thank you everyone for helping me, and, once again, sorry for being SUCH a noob. I hope there will be people benefitting from this LONG (yet complete -- I hope) walkthrough. I hope you will spend much less time fixing your wireless network than me.
Cheers