The current release is 1.0
When you open Edge Animate, the Welcome screen should say Adobe Edge Animate 1.0, over a purple striped banner at top left of the page.
You can also check the toolbar here: "Edge Animate/About Edge Animate", to check the exact build (current build is 18.104.22.168.21541).
To download this build, create a Creative Cloud account, and download Edge Animate for free!:
I assume update notifications will occur the way they do for other Creative Cloud installments- via a notification from the Adobe Application Manager. Generally it appears as a bubble notification.