Can a lunar eclipse completely 'turn off' the mooon, i.e. like a New Moon? Or is it always just a 'shading' of the moon (sometimes red in color)?
Lunar eclipses are caused when the Moon is in opposition to the Sun. Normally this produces a full moon, but if the Moon is in exact opposition (considering incline of the Moon's orbital plane), all direct sunlight will be blocked from the Moon:
So if all the sunlight is blocked, how can we see the Moon? Well, the main reason is that sunlight is often dispersed in the atmosphere, and so it can reach the Moon. In addition, there's airglow, which is when sunlight hits Earth's upper atmosphere and causes multiple chemical reactions, scattering light throughout the night sky.
Thus, all this light from Earth, called earthshine, reflects off the Moon and illuminates it. In addition, Earth removes and blocks parts of the sunlight's spectrum, leaving only the longer wavelengths. This causes the Moon to appear red. Lastly, because the Earth blocks off all the direct sunlight from the Sun (only diffracted sunlight and airglow reach the Moon), we can actually see Earth's shadow on the Moon.