Well, lets take this one step at a time.
1) When you did uname -r, you got 2.4.22-1.2115.nptl which is the kernel version. You need to get the kernel source that matches this. The kernel source you installed is 2.4.20-9 which is not the same. So, download and install the kernel-source-2.4.22-1.2115.nptl rpm. (Note that the 2.4.22-1.2115.nptl kernel is a couple of releases old).
2) Since you downloaded the nforce-1.0-0261.tar.gz forget about the NVIDIA_nforce-1.0-0261.rh90up_2.4.20_9.athlon.rpm rpm file because it is an old rpm that does not match your current kernel. Extract the source code from the tar.gz file into a directory using
tar -xvzf NVIDIA_nforce-1.0-0261.tar.gz
Then cd (change directory) to the nvnet source directory
Then type in the commands as root
Assuming that you have the current development tools installed and things have gone right, the nvnet module should be built and installed for your current kernel. You can check that it is there by:
ls /lib/modules/`uname -r`/kernel/drivers/net/nvnet.o
If it is found, the nvnet kernel driver is there for use.
3) Make sure that the entry is made in the /etc/modules.conf file with the command as root:
grep nvnet /etc/modules.conf
If the output is "alias eth0 nvnet" good, otherwise edit that info into the /etc/modules.conf file.
4) Now the easiest way to proceed (for a newbe) is to reboot the box into Linux. This is not necessary but does check that the nvnet module will be loaded when the computer is booted and inserts it into the running kernel.
5) Configure your networking with the tool of your choice. e.g. System Tools -> Network Device Control or redhat-config-network.
If you update the kernel in the future, just keep the kernel, kernel-source updated together and go to the nforce/nvnet directory. Do the 3 make commands and you are up and running.
Hope this helps .... someone at least