Offline editing is part of the upgrade. If you're upgraded, when you're working on a script and you disconnect or lose connection for the first time, you are asked whether to continue offline. You can choose to do this automatically.
Note that you don't have to have done anything before - unlike Google Docs etc YouMeScript doesn't expect you to be able to predict the future of your internet connection.
When you reconnect, if you haven't closed the tab, your changes will automatically synch. This may take a moment or two if you've made extensive changes. If you have previously closed the tab, you'll be asked whether you want to resynch or save your work to a new file. You can choose to resynch automatically in future.
The options to continue working offline and to resynch automatically can also be specified through "Offline..." in the option (cog) menu.