There are many ways to get Maxima, and the choices are governed somewhat by the user's operating system (although Maxima proper is platform independent). The home page for Maxima (which has links to download from SourceForge) is
This document was written with Emaxima on GNU-Emacs. Emacs is a powerful text editor, and Emaxima uses Emacs to integrate Maxima input/output with LATEX code to produce documents that look like they could have come from a textbook. That's why the mathematical expressions below are so pretty. See the following link to learn more about Emaxima.
If you do not want to write a paper but just want to work with Maxima interactively then another option is imaxima, which also works with Emacs and LATEX (and Ghostscript) to typeset Maxima input/output professionally. To learn more about imaxima see the following.
Another option that exists is TeXmacs, but I do not have much experience with it. From what I can gather it has a good reputation.