
vogonWild
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Height map - We simply are taking the vertical distance to use to reinforce our sea level

Noise Map - this is generating values between 0 and 1. The black spots are closer to 0. Because this is 3d noise, there are values for the points inside the cube as well.

Multiplying the height and the noise together gives us this result. Values further down are more likely to be solid, and further up more likely to be air.

Passing the combined map into a greater than operation, we are able to get a definitive solid ground. Note that there is a tunnel in the side of this.

By removing the values identified by our previous step, we can now see the landscape starting to form.

Using the value of the height, we can determine a simple coloring scheme to make this look like grassy mountains.

A simple box is added in to make the sea level.
This video shows the same process above, but used to generate a spherical planet. The only major difference is the swapping of a linear gradient, to be a spherical gradient for the height map.
You can notice the cave in the left side of the crust here.
This is another seed showing the same as the previous video.

This was created in Blender, using a relatively simple set of nodes.
The values in the Input Geometry section give us 3d coordinates to map to our noise and height values. We multiply the noise by the height, and then scale it over time for the spherical animation. We take this output and plug it in to a "greater Than" operation, which gives us our solid ground, and plug that value into the density. We also multiply that value to make the ground appear more solid. The height map is passed through a color ramp to determine the color of the planet at a given height.
Many of these values are very rudimentary, and with a little tweaking, or a few more layers of noise, something much more interesting can be achieved.

As an accidental added bonus, here is an infnitely repeating loop of a sheet of color traveling over 3d noise.
Vanonym
Very comprehensive post, thank you! I might use this for some projects