The short answer to your question is that you simply can't open .exe files with OS X, but don't stop reading here. The reason you can't open an .exe is because the OS X and Windows operating systems use different and incompatible coding. However, there are a few ways in which you can use Windows software on your Mac, MacBook, Mac Mini or iMac.
Mac OS X software
Before you opt for a complicated method you should firstly check whether there is an OS X version of the software you are trying to install. Many programs are developed for multiple operating systems so you may have just downloaded the Windows version rather than the one for OS X.
If the software is specifically for Windows then read on and use one of the methods detailed below.
The first way to use Windows software on your Mac, which must be Intel-based, is to use Boot Camp. It allows you to install Windows as a secondary operating system on your Mac, resulting in a dual-boot system.
This comes pre-installed on OS X 10.5 Leopard and later so search for 'Boot Camp Assistant' or navigate to the Utilities folder.
This will then guide you through the process of installing Windows on a new partition on your hard drive. The latest version of Boot Camp (4.0) supports Windows 7 Home Premium, Professional and Ultimate but not XP or Vista.
Once the installation is complete you can simply choose which operating system to use when you start your Mac.
The second option you have is to buy and install virtualisation software such as Parallels or VMware Fusion on your Mac. This allows you to run Windows inside Mac OS X on a virtual machine; therefore you can run both operating systems at the same time.
When using virtualised Windows you can open .exe files like you would on a Windows PC.
Another method is to emulate Windows within OS X using Mac software like CrossOver. Unlike the previous options, this doesn't require a Windows licence to work. The drawback here is that not every Windows application is supported so it's worth checking beforehand.