How to edit .woff font files offered by Google Webfonts?

There's a free, cross-platform tool called FontForge, which can be used to create, edit, and view a wide array of font types.

Homepage: http://fontforge.org/
Github: https://github.com/fontforge/fontforge/

Here are some screenshots of it in action:

WOFF

WOFF2 ^{(added in 2018)}

Editing Characters

Convert the 'woff' webfont to a regular font (e.g. TTF) using a service such as Online Font Converter. Then edit the converted file with your favorite font editing software.

Specific 'woff' Editor:

http://www.high-logic.com/font-editor/fontcreator.html

Programming Tools:

http://www.freetype.org/