You know that one side of the moon always faces us. So you’d have to be on that side to see any Earth at all. But from any part of the moon’s near side, you could see Earth wax and wane – just as the moon does as seen from our world. Both the Earth and the moon are always half illuminated by the sun. But from either world, at any given time, you can see varying portions of that lighted half – or various phases of the Earth or moon.
The phases are always the reverse of each other. When we see the moon as nearly full, any moon people would see a slim crescent Earth. When we see a completely full moon, the moon, Earth and sun are in a line – with Earth in the middle. Then people on the moon wouldn’t see Earth at all because it’d be hidden in the sun’s glare.
Also consider the moon’s slow rotation. The moon appears to rise and set as seen from Earth not because of the moon’s motion – but because Earth spins once a day on its axis. Because one side of the moon always faces us, from most places on the moon, Earth doesn’t appear to rise or set. Instead, from a given point on the moon’s near side, you’d always see Earth hanging in your sky. Meanwhile, the sun would rise and set once each month – each time the moon spun once on its axis, thereby keeping that single face turned toward Earth. So from any spot on the moon, day and night would sweep over you once a month.