Monodevelop is the default code editor with Unity, but if for some reason you don’t want to use it (or can’t), here’s a quick video showing how you can switch to something else.
Here are some optional editors:
Komodo Edit (Windows and Mac, free)
Sublime Text 2 (Windows and Mac, commercial w/unlimited trial)
After I created that video for someone who was having the problem, I discovered the real problem. They were selecting the script in Unity and the Inspector would show the code; they were trying to edit the code right there in the Inspector, which is a read-only view of the code.
Once they double-clicked the script it opened in MonoDevelop and all was good. However, for people who prefer a different editor, the video above is still the way to do it.