I uninstalled my student version of Solidworks and I can not figure out how to reinstall the program.

just restart and install the way you did when you first install it

How much time passed between installs? I believe there is a limit to expiration of the student license. Also, is this being reinstalled on the same machine? If so, it may be reading some info from your computer's registry that is giving the impression that it has already been installed.