rsync
You don't need an Apple Script, OS X comes with an old command line utility called rsync. For a really basic backup, just run "rsync -a /Users/username /Volumes/externalharddrivename/" in your terminal.
Note the lack of a trailing / on the first path, this is important. A trailing / means "the contents of" rather than the folder itself. So with a trailing /, all of the contents of your home folder would be dumped onto the root of the external hard drive, without a copy of the folder itself.
Run the same command again, and only the files that have changed will be moved. By default, files you've deleted in your home folder will not be removed from the backup, add "--delete" right after the "-a" if you want deleted files to be removed from your home folder. rsync is very powerful, if you want more information, run "man rsync" in your terminal.