If you have already set up your own WordPress blog, right from the beginning you will probably have the tools you need to get started with WordPress MU. All you need is a plain text editor and an FTP client. As your experience grows, you may find that you want to add to your arsenal some other tools such as browser plugins that will help you tweak and debug your site from within your browser.
For Windows users, I recommend one of the following text editors:
Notepad++ (http://notepad-plus.sourceforge.net)
Crimson Editor (http://www.crimsoneditor.com/)
Both of these are free applications. (Notepad++ is open source.)
For Mac users I recommend Aptana (http://aptana.com/). Linux users can try JEdit (http://www.jedit.org) or see if their favorite text editor has syntax highlighting capabilities.
For an FTP client, I recommend FileZilla (http://filezilla-project.org/). This FTP client is free and has versions available for Windows, Mac, and Linux...