Corona does not have a designated program editor to code in so you will have to find one that suits your needs.
For Mac OS, TextWrangler is a good one and free too! You can download it at http://www.barebones.com/products/textwrangler/download.html. Other text editors such as BBEdit at http://www.barebones.com/thedeck and TextMate at http://macromates.com/ are great, but you will need to purchase those in order to use them. TextMate is also compatible with the Corona TextMate Bundle: http://www.ludicroussoftware.com/corona-textmate-bundle/index.html.
For Microsoft Windows Notepad++ is recommended and can be downloaded at http://notepad-plus-plus.org/ or Crimson Editor at http://www.crimsoneditor.com/. Both editors are free.
Any text editor, such as TextEdit for Mac or Notepad for Windows, that is already included in each operating system works as well, but it'll be easier to work with one that is designed for programming. For Corona, using an editor that supports Lua syntax highlighting will work the best when coding. Syntax highlighting adds formatting attributes to keywords and punctuation in a way that makes it easier for the reader to separate code from text.