when I was a candidate, I had my first round with McKinsey as a video interview, since I was applying to an office on another continent. During my time with McKinsey, I then interviewed dozens of candidates via the Firm's Video Conference System for various offices across the globe. So here are a couple of points that I would recommend:
1. Be ready early! It might take some time to get the Skype going and ensuring all components (camera, microphone) properly work. You don't want to have the interviewer waiting at the other end (even if it is not your fault)
2. Remember to turn off or silence your phone before starting the Skype session. Shut out all distractions, and give yourself around 10 minutes to collect yourself.
3. If it helps you, a video interview gives you the opportunity to bring a "cheat sheet" with a couple of bullet points (e.g., PEI stories or critical issues you want to highlight) and place it in a way that you can read it but it is not in the angle of the camera (maybe fixed on the wall behind the laptop). Just don't stare at the page during the interview - this might feel odd.
4. Look directly into the camera! You might be tempted to look at the monitor or yourself, but focus on making eye contact with your interviewer via the camera.
5. When responding to questions from the interviewer, nod, but take a second before responding in case the connection is weak — so that you don’t end up talking over the interviewer.
6. Double-check your body language! A video interview has the advantage that you can see yourself. So it allows you to more easily keep an awareness on your body language and that you keep the right level of "projection" during the interview.