How do I edit an existing tag message in git?

To update a complex message, just specify the annotated tag option with -a or the signed tag option with -s:

git tag <tag name> <tag name>^{} -f -a

This will open an editor with the contents of your old tag message.

git tag <tag name> <tag name>^{} -f -m "<new message>"

This will create a new tag with the same name (by overwriting the original).