When I first pondered folding a regular octagon. I immediately thought, "How simple. Start with a square piece of paper and fold the corners in." But once I tried it, I realized that the difficulty with this approach is knowing how far to fold the corners. This project shows you another method altogether.
Fold the square in half along both diagonals to find the middle of the square. Open.
Fold all corners so they meet in the middle. Open.
Fold an angle bisector of the angle formed by the creases you just made and the edges of the paper.
These creases form a regular octagon.