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 it is free too! You can download it from 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 them in order to use them. TextMate is also compatible with the Corona TextMate Bundle, which is available at http://www.ludicroussoftware.com/corona-textmate-bundle/index.html.
For Microsoft Windows, Notepad++ is recommended and can be downloaded from http://notepad-plus-plus.org/.
The following are the text editors that are compatible with both Mac OS and Microsoft Windows:
Sublime Text (http://www.sublimetext.com)
Lua Glider (http://www.mydevelopersgames.com/Glider/)
Outlaw (http://outlawgametools.com/outlaw-code-editor-and-project-manager/)
Any text editor, such as TextEdit for Mac or Notepad for Windows, that is already included in the 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 the 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.