Although, this requires 'QuickTime Player' which I think is Mac exclusive, so if you own a PC or another computer you will have to find some other method.
TL;DR version of the webpage:
- Plug your phone into your computer using the charger (a.k.a 'lightning connector')
- On your computer, open the pre-installed app, 'QuickTime Player'
- Go to File at the top of the screen and click "New Movie Recording"
- Click the drop down menu directly to the right of the red record button
- Look at camera options and select the name of your phone
And that's it. Your computer can record both the audio and the screen, so it should work well. I'm testing it for real later today, and can let you know if there are any problems.