These are a few ways that ice was and is made, which I learned from the awesome book Ice: The Nature, the History, and the Uses of an Astonishing Substance by Mariana Gosnell.
The first way is just like making ice cream the old-fashioned way: snow or cold water mixed with salt can become colder than freezing. So if you put a cup full of water (or ice cream ingredients) and stir the supercooled salt/water mixture around it, the water in the cup can turn to ice.
Expansion of Gases
As vapor and expands into a large space the molecules speed up, and to do so they take heat from the surrounding environment. This is similar to how evaporation of sweat cools you off - the liquid turns to gas and expands into the air.
Early ice machines taking advantage of this property used pistons that compressed air then released the pressure. The air expansion would pull heat from its surroundings - in this case a container of salt water - and that salt water would turn a pan of water into ice.
The next generation of ice machines used other gases instead of plain air- ether and ammonia for example. They still do.
Vintage Block Making
The Ice book also described an ice block-making operation from the Millersburg Ice Company in Ohio. They use large metal pans filled with city water that are lowered into a lake of salt water cooled to 12 degrees Fahrenheit. The pans of water then freeze from the outside-in.
Into the center of each pan they put an air hose to keep the water moving. As ice likes to be a pure crystal, the ice forming first is crystal clear, leaving most of the minerals in the water trapped in the liquid center portion. Before the block of ice fully freezes, they suck out the mineraly water and replace it with more city water. They say it looks less cloudy this way, though the center core is still a bit cloudy.
Making Ice Cubes - Bag Ice Method
Some commercial ice machines make ice in the following way: Water runs across vertically-positioned, cooled plates. Ice forms on the surface. When it reaches the desired thickness, they poke it with knobs that break it up into cubes. This ice is bagged and sold.
Making Ice Cubes - Clear Method
Other ice machines make clear cubes in the following way: Regular water is sprayed upwards onto cooled plates. The plates are cooled only to 32 degrees Fahrenheit - freezing temperature. At this temperature water freezes but minerals generally do not, thus the minerals drain off while the ice that freezes is nice and clear.
Making Flaked Ice
Flaked ice is the kind you see at fish markets- smaller than cubes but less dense than crushed ice. This is made in a machine that sprays water onto a cooled, rotating drum. After just a thin layer of ice forms, the ice falls off the drum and shatters.