Heat a piece of square stock up to forging heat. Place it on the anvil with the end of the stock lined up with the edge of the anvil. Point it down slightly toward the top of the anvil and strike it with the flat face of the hammer angled slightly further with respect to the anvil.
The effect is to pinch the end of the stock between the hammer and the anvil. We want the hammer to have room to go a bit past the edge of the anvil, so the center of the hammer face is striking the area to be pinched.
After a couple of strikes, rotate the stock by 90°, align and strike as before. Gradually the square stock will narrow into a skinny pyramid shape. Continue this until the stock stops glowing and cools down to the point it no longer flows with a smushy sound and feel, but springs back crisply and clangs.
It's time to reheat the end, just as at first. Continue with forging and reheating it until the end narrows to a point.
This is a basic point, used for fireplace pokers and all sorts of tools.
For a round point, rotate the stock by 45° and forge as before, with a few light strikes, then rotate by another 90° and forge a bit more. The 4-sided pyramid becomes an octagonal pyramid. By forging very lightly on the corners of the octagons, the shape will be close enough to round for most purposes.
Next Chapter: Exercise 2: Hot Cutting