The stars are there! They're just too faint to be seen.
This is usually the first thing HBs talk about when discussing the Hoax. That amazes me, as it's the silliest assertion they make. However, it appeals to our common sense: when the sky is black here on Earth, we see stars. Therefore we should see them from the Moon as well.
I'll say this here now, and return to it many times: the Moon is not the Earth. Conditions there are weird, and our common sense is likely to fail us.
The Moon's surface is airless. On Earth, our thick atmosphere scatters sunlight, spreading it out over the whole sky. That's why the sky is bright during the day. Without sunlight, the air is dark at night, allowing us to see stars.
On the Moon, the lack of air means that the sky is dark. Even when the Sun is high off the horizon during full day, the sky near it will be black. If you were standing on the Moon, you would indeed see stars, even during the day.
So why aren't they in the Apollo pictures? Pretend for a moment you are an astronaut on the surface of the Moon. You want to take a picture of your fellow space traveler. The Sun is low off the horizon, since all the lunar landings were done at local morning. How do you set your camera? The lunar landscape is brightly lit by the Sun, of course, and your friend is wearing a white spacesuit also brilliantly lit by the Sun. To take a picture of a bright object with a bright background, you need to set the exposure time to be fast, and close down the aperture setting too; that's like the pupil in your eye constricting to let less light in when you walk outside on a sunny day.
So the picture you take is set for bright objects. Stars are faint objects! In the fast exposure, they simply do not have time to register on the film. It has nothing to do with the sky being black or the lack of air, it's just a matter of exposure time. If you were to go outside here on Earth on the darkest night imaginable and take a picture with the exact same camera settings the astronauts used, you won't see any stars!
