To make Java run an external application,
you should use the Runtime.
Read this JavaWorld article to get a good working start.
I have a feeling, though, that that is not quite what you want to do, so you will have to be a bit more specific.
And just to nitpick:
"running exe files with Java ... on any computer"
If the computer isn't a Windows computer, then you can't expect it to run exes.