So I have been taking a few classes on python and the whole time, I was wondering about modules. I can install them and run them with Eclipse but if I compile that program, so if it has an 'exe' extension, how would the module react on a computer that doesn't have it installed.
Example:
If I made some random little thing with something like pygame. I installed the pygame module on my computer, made an application with the pygame module and compiled it into an executable, how does the other computer that I run that file on. Or does it not work at all?
Python modules are already executable - you don't compile them. If you want to run them on another computer, you can install python and any other dependent module such as pygame on that computer, copy the scripts over and run them. 
Python has many ways to wrap scripts up into an installer to do the work for you. Its common to use python distutils to write a setup.py file which handles the install. From there you can use setup.py to bundle your scripts into zip files, tarballs, executables, rpms, etc... for other machines. You can document what the user needs to make your stuff go or you can use something like pip or distribute to write dependency files to automatically install pygame (and etc...).
There are many ways to handle this and its not particularly easy the first time round. For starters, read up on distutils in the standard python docs and then google for the pip installer.
Python modules on different devices