To use Jade or BSim locally in standalone mode, simply run
python server.py
to start a basic HTTP server listening on port localhost:8000. server.py is compatible with both Python 2.7+ and 3.6+. You can access the tools at
http://localhost:8000/index.html
and click on the link to access that Lab's Jade or BSim tool.
In the standalone version of the tools, changes are saved to the local server as they're made. The saved state is for the particular .html file you accessed, so if you have several .html files for, say, different projects, their state will be stored separately. Next time you browse to the URL above, you'll be able to pick up your design where you left off.