All of these start out as air with a lot of water vapor in it - called moist air, or humid air. Then the water vapor collects around dust particles to form tiny drops of liquid water, so small in size that they don't plummet down to the ground right away but instead float around as clouds, pushed around by the wind and by hot or cold air as it rises and falls.
Then it takes one of three steps, eventually going down a path that will lead to rain, snow, or hail.
If it will become rain, the cloud of droplets gets gradually colder and denser, and the tiny drops of water come together to form larger drops. Eventually, these are too large to "float" on the air currents, so they begin to fall. This is what happens when it rains.
If it will become snow, the "rain" goes through a layer of air that is very cold - below freezing. The rain drops freeze into tiny flakes and fall down to the ground as snow.
If it will become hail, the "rain" drops fall down through a layer of cold air, but are pushed upward by a draft before they reach the ground. So they freeze, then melt again. When they are pushed upward into a cloud, tiny drops of water form on the outside of the melting hail, and weigh it down more so that it falls. This can happen again and again to a single piece of hail - it falls, melts, is pushed upward, re-freezes with an extra layer on it, falls, melts . . . kind of like an onion with lots of layers. Eventually, of course, it falls down to the ground.
This, by the way, is why you can cut a big piece of hail in half with a pocket knife to see the layers of ice that formed as the hail fell.