What is the correct syntax to assign a value to a boolean client tag?

If you're talking about scripting, then you'll use something like:

system.tag.writeToTag("[Client]path/to/tag",1)

More information can be found in the user manual, appendix C under the system.tag library. One more note, as of 7.5 the function name has changed to system.tag.write. Both will work, but the replacement is preferred. Let me know if you have any more questions.

I have a property bound to this client tag.

How would I figure out what property threw a property change event?

Are you talking about within an event handler script? You would call event.propertyName to see which property changed. For an example, look at the "propertyChange Events" section at the bottom of the page of this link:

http://inductiveautomation.com/support/ ... _types.htm

That property change would be what you want to occur or condition to exist that will make that boolean go from 0 to 1. If you have something bound to that tag, say a script or a query, and you want to run it when that boolean >0, you could have that on a button. That is just an example, your going to want it bound to whatever you want to trigger the change of that client tag.