What will a lunar eclipse look like from moon? Will earth become a completely dark circle?
It would look like a solar eclipse! What happens is that Earth gets in the way between the Sun and the Moon. From Earth we see the Moon disappear, from the Moon one would see the Sun disappear.
Earth is fix on the Moon's sky, because the Moon always turns the same side towards Earth. Earth as seen from the Moon has phases, like the Moon has when seen from Earth. You would see the Earth crescent waning and becoming completely dark as the Sun moves towards it and disappears behind the then invisable Earth. While as seen from Earth, the Moon and the Sun have the same size on the sky, when seen from the Moon Earth will look almost 4 times larger (in diameter) than the Sun, so solar eclipses will last that much longer and be more common than on Earth.
Yeah, you'll see earth as all dark, if it is total lunar eclipse.
In a Lunar eclipse earth comes in between the sun and the moon. Because of this, the sun rays don't reach the surface of moon.
Now answer to your question:
As earth's sunward side is blocking light the other side will be darker. As you are standing towards shadowed side of earth, you cannot see earth at all.
All above explanation is accurate in the case of a total lunar eclipse.
During a lunar eclipse on Earth, the Sun would be eclipsed by the Earth as seen from the Moon:
What this animation does not show is the corona around the Sun (which would be partially visible when the sun has been occulted) and the reddish ring of light that would encircle the Earth due to the sunlight refracted by the atmosphere of the Earth.
Unlike a solar eclipse as seen on Earth, the stars are always visible since there is virtually no atmosphere on the Moon. Of course, until the Sun is totally occulted, it would be hard to see stars close to the Sun and the solar corona due to the brightness of the Sun. Furthermore, the Earth is 4 times as large as the Moon and so would cover most of the corona (or possibly all of the corona if the eclipse is central).
It would look like this (actual picture of the Earth, seen from the Moon, during a lunar eclipse):
Link to full page: http://apod.nasa.gov/apod/ap140407.html
The Earth would appear surrounded by a bright ring, even though the Sun is completely hidden behind it. The ring is sunlight refracted through the atmosphere. It's basically all the sunrises and sunsets, seen at once.
The Earth would never appear fully dark. The bright ring around it will always be there. This is due to the atmosphere.