I understand that it is the Earth’s shadow that causes moon phases. This works except for one problem, this morning the sun and the moon were out at the same time, which isn’t unusual except this time it dawned on me that if the whole Sun is out above the earth and the whole Moon is up above the Earth how is there still a shadow over the moon? Wouldn’t it have to be a full moon because the full sun is shining on it now? Or why wouldn’t the moon phases be horizontal instead of vertical?
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The Earth’s shadow is not what causes Moon phases.
At any given time, half the Moon is lit up by the Sun (just like half the Earth is). If that side of the Moon faces the Earth (which happens when the Earth is roughly in between the Sun and the Moon), you get a full moon (or occasionally a lunar eclipse when the vertical axis lines up perfectly too). If that side of the moon faces away from the Earth, you get a new moon (and occasionally a solar eclipse when the vertical axis lines up perfectly too). If it’s somewhere between those extremes, you get a crescent, quarter, or gibbous moon.
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