Just press [Ctrl]+[Alt]+[Shift]+[R] keys to start/stop recording. When recording, a red recording symbol will appear at the right side of Gnome’s top panel.
The resulting webm video will be saved to your Videos folder.
GNome WIll save as WEBM
Gnome will only write it out to webm which is a pretty standard format for playing and sharing on the web, the major web browsers support webm too as it’s the HTML5 video standard.
But if you need it in a different format I can recommend the video conversion tool Transmaggedon which is very easy to use and can be found by simply searching from your Gnome desktop overview and selecting it to install from the Software application.