Holding the paper upright, fold it in half horizontally. Turn it 90 degrees, then fold it in half horizontally again. Turn it another 90 degrees and give it another fold.
Fold it in half twice more, paying particular attention to the rigidity of the corners. For the last fold, you'll probably need to bend the paper into a U-shape to start, sort of like a piece of celery. When bent, crease it in the middle with your thumbnail. Then fold it hard and press it all together firmly.
Hold the paper in your dominant hand. With your other hand, hold the bottle firmly at the neck. The top of this hand should be covering one side of the bottle cap. The bottom of the bottle should be on a stable surface like a counter or table.
Pinch the paper hard between the pad of your thumb and the side of the second knuckle of your index finger with your dominant hand. The folded corner should be facing up towards the ceiling. Position this folded corner right beneath the edge of the bottle cap.
Use the paper to firmly and steadily pry up the side of the bottle cap closest to your dominant hand. At the same time, use your other hand to stabilize the bottle on the table and hold down the other side of the bottle cap to help you get more upward force from the paper.