A "tar" file is just an image of a directory. You use the tar command to recreate that directory structure on your hard drive.
In your case, since you're using Mint 15, go to the Accessories menu and open the archive manager. When the manager window opens, click on the Open button, and open the tar file. Once it's opened, extract it to a folder on your hard drive. Close the archive manager, open a terminal window, and cd to the directory into which you extracted the file.
In the extracted directory (if it is a "standard" software distribution) you should find a text file called INSTALL which you should read and exactly follow. If what you have is "standard," you have a copy of the source code for the driver, which you will have to compile, link, and install in your kernel.
In order to compile the code you will need to have installed the gcc package, and the kernel-devel package, although - since Mint is Debian based. those should already be there.
Note that your life would be much simpler if you located the dpkg for the driver you need in the Mint repositories, or one of the upstream ones. (Check your package manager options to see if you have other repositories that you could activate.)
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