A demo site is available for you to get an impression about the system.
You can now register your own user account at this demo site.
Please provide an email address and a password. A registration code will be emailed to you.
Then you can return to the login screen and login with your username and the password+registrationCode.
Now you can enroll a token like a Google Authenticator or register your U2F device.
If you experience any difficulties, drop me a note.
If you prefer a simple hosted solution for more elaborate tests, you can got to the partner D9T, who provides simple a hosting solution, where you can simply start your own system.
You can also go to NetKnights, who provide privacyIDEA Enterprise Edition and get your own privacyIDEA testing instance.