What you have downloaded is a little chunk of code that can be added to the kernel of your system to provide support for you network card. However, its probably already there in another form.
If there is already a module present then you might want to try running modprobe via-rhine
to load the module. If this works then you may get some messages or just get returned to the command prompt. If it doesn't work then you will get a clear error message say that it couldn't find the module.
If you get the error message the you will need to recompile your kernel to include 'Via Rhine' support, you'll find this under the 'Network Devices' section of the kernel config. Have a look at http://www.linuxdoc.org/HOWTO/Kernel-HOWTO.html
for details of kernel compilation. This will seem quite scary at first, but its not really that bad!
You can sometimes download modules (read drivers) that are precompiled but they will only work with a specific kernel and a single architecture so its unusual to find them. You normally get the source and need to compile it yourself.
Have a read of the HOWTO and post your specific queries. You can always look through your kernel config and then not save the changes without any risk of screwing things up! If you do post questions about a kernel compile be sure to include the version of the kernel you are using and the distro.
good luck! Once you get the card recognised you then need to get the network up... Again check out the howtos on http://www.linuxdoc.org
its all there for the taking.