EXE files are Microsoft executables; using them runs a Windows or DOS program. Mac OS does not support such programs, but sometimes Mac-supported files (like images or sound) are stored within EXE files, and the format is often used on Windows computers as a "self-extracting archive," the contents of which are readable on a Macintosh.
Open your Mac's terminal by going to "Applications," "Utilities" then "Terminal."
Navigate to the location of the EXE file using the "LS" command to list directories and the "CD [directory]" command to enter them. (If your file is on the desktop, simply typing "cd desktop" from the Terminal prompt should be sufficient.)
Type "unzip [filename.exe] -d [directory]" and press "Enter." For example, to unzip the archive "foo.exe" to the new directory "unzippedfoo," type "unzip foo.exe -d unzippedfoo."
The contents of the archive will now be in the directory you created. If the Unzip utility returned an error, the EXE file was probably not a self-extracting archive, but an actual program executable that is not compatible with Mac OS.
Windows programs can be run on an Apple computer by installing a copy of the Windows operating system using Apple's Boot Camp utility. See Resources for a link to Apple's official guide to Boot Camp.