Per the video's description, he says to fold the paper vertically (or "hot dog style," to use an elementary school throwback) "until you end up with only a small amount of paper left." Then, he says to fold that dense strip in half horizontally ("hamburger style") so you have a shape that looks like a pointed V, which you can then use to apply pressure, in one steady motion, to the underside of the bottle cap.

If you don’t have paper handy, you can pry under the cap with the prongs on a smartphone charging brick. If your charger is expensive, you might want to try a cheap pair of sunglasses by positioning the gap that usually rests on the bridge of your nose against the lip of the unopened bottle, as the shape of that curved V mimics an actual opener. If all else fails, purchase beverages with twist-off caps.