You can download Mugen at Elecbyte's site: http://www.elecbyte.com
If you want to make characters, backgrounds ... you also need to download all things in the Developper section and read Mugen docs.

Note: The current version is for Linux only. If you want to run Mugen on Windows, you need to download an older version of Mugen (just use a search engine to find one).
Note 2: There is a new version of mugen for Windows called WinMugen, but it's not official. So I don't recommand using it.