Soft U2F currently works with Google Chrome and Opera's built-in U2F implementations, as well as with the U2F extensions for Safari and Firefox.
When a site loaded in a U2F-compatible browser attempts to register or authenticate with the software token, you'll see a notification asking you to accept or reject the request. You can experiment on Yubico's U2F demo site:
Interested in learning more? Head over to our Engineering Blog and read more about the motivations for the project plus the security considerations of hardware vs. software key storage.