Pro Tip: Demo On-screen Using Real iPhone
This post actually contains two Pro-Tips. They are summarized by the boy scout motto: Be Prepared.
First, always carry a cable for your iPhone. Always. I was in an important meeting once and an associate was suddenly asked if he could show something from his iPhone. He couldn't because he didn't have his cable on him, therefore couldn't plug in and demo what he needed to from the iPhone. Fortunately, I had one coiled up in a pocket, swiftly shifted it to him, and he was able to present as expected. The day was saved... or at least the meeting. It turned what would have looked like bumbling inept bozos into pros.
This part is the meat and potatoes of this Pro Tip. One of the simplest ways to show your real iPhone on screen is to connect it to your computer via the cable you deftly fetched from your nerd-pocket and then start QuickTime Player. From QuickTime Player's File menu select File > New Movie Recording... and at the center of the screen a control will display with a red circle button, to the right of that button is a downward white chevron arrow, click that and select your iPhone. Now your iPhone's screen is streaming right onto your computer screen and you can share however you want at this point.
Don't be caught in a meeting with your pants down - always expect to present what you're working on and have a way to do it. Yoda says "do or do not..." If you do not, it's probably because you didn't prepare.