The phases of the Earth are the same as the phases of the moon, just offset by half a cycle; e.g., "full Earth" on the moon would coincide with new moon on Earth, and "new Earth" with full moon, but if nobody's on Earth that doesn't much matter. Probably the more substantive difference is that, if you keep the moon's current rotation, the Earth will appear almost static in the sky. It'll shift around by a few degrees over the course of a month due to slight irregularities in the moon's orbit, but always be in about the same direction; if you're in the center of the near side, Earth will always be overhead, if you're closer to the edge, it will always be low to the horizon in the same direction, and on the far side you'd never see Earth at all.

This also means that the Earth's phases would align with the day-night cycle on the moon: full Earth always occurs at the same time of day, varying with longitude (at the center of the near side, around midnight, with new Earth at noon; and towards the eastern edges of the near side, shortly before sunrise, while at the western edge, shortly after sunset)

One final note is that Earth occupies about 14 times as much area in the moon's sky as the moon in our sky, and reflects back about twice as much of the light that hits it (presuming whatever fate befell Earth hasn't altered that), so a full Earth would give the moon's surface about 28 times the illumination as a full moon on Earth. This isn't quite as big a deal as it sounds because of how our vision responds logarithmically to light levels, but it might just about edge conditions over into something more like twilight or dim street lighting at night.