You can do it!
Here's what you need to do.
In the window that appears, select the checkbox. Also note the highlighted portion of the text.
You'll see "sharing" in the title bar.
Repeat the previous steps to unshare. You'll see this message.
I don't have a network right now to test and get screen shots on but I tested it during a previous class with a network. Essentially updates of other people's tasks are displayed when you save. Sometimes before. And sometimes there is a lock from another person but only temporarily.