Recording your iPhone or iPad screen into a video file has never been easier! with the latest version of Mac OS X, you can record your iPhone using QuickTime Player.
You just have to connect your phone to your your Mac OS computer using the lightning cable that came with your iPhone/iPad, and then run QuickTime Player on your Mac!
The next step would be to select File Menu>Record new movie, and select your iPhone/iPad from the arrow as shown below:
Now hit the record button
And start using your phone as usual while recording it into your Mac
And to save the recording, just close the recording window and it will ask you to save the video file.
You can see a step by step video below: