Just download the driver package and unzip it.
In the files you just downloaded there will be a readme.txt file. Read it. It will describe pretty much step by step what to do.
You see the goal here is to take the source code (original programming code written by the programmer) of the driver and compile it into a usuable binary. The trouble is is that unlike Windows were you just have to deal with 2 or 3 different kernels for win9x or winME or Win NT or XP, each different Linux flavor has it's own version. So it's hard to make a "universal" driver. So instead they give you the code for it and you have to build it yourself.
They give you 2 methods of handling the source code. The more correct way for you since your using Redhat is to use the RPM. Which is Redhat Package Managment file, but using the tarball method should work, too. Just follow the directions and it should work out.
After you get the module up and running (linux word for driver) by using "insmod bcm4400" or "modprobe bcm4400", you can manually get your network going.
If you have a DHCP server you run the command "dhcpcd eth0" in a terminal and that should get you going. If not the manual way is
ifconfig eth0 your.ip.address
route add default gw your.gateway.ip.address
To set up DNS you need to make sure that you have your DNS server recorded in a configuration file "resolv.conf". You can manually edit the file to make sure it's there our you can use this command to add it to end of it. (parathesis in this case are important)
echo "nameserver your.dns.server's.ip.address" >> /etc/resolv.conf
If not these drivers don't work out for you... well Nic cards are cheap and you can probably pick up a realtech-based one down at a local store for 8-14 dollars that will work just fine.
Hope it works out for you.