Three crew members set out for the Moon
Apollo 8 carried Frank Borman, James Lovell and William Anders. A Saturn V launched them on December 21, 1968, and the spacecraft subsequently departed its Earth parking orbit for the Moon.
The mission used the command and service modules without a lunar module. Navigation, communications, life support and propulsion had to take the crew into lunar orbit and bring them safely home.
References: [1]
An engine burn behind the Moon
On December 24 the spacecraft passed behind the Moon, temporarily out of radio contact. The service-module engine fired to slow it into lunar orbit. When communications resumed, the ground confirmed that the crew had arrived.
Apollo 8 completed ten lunar revolutions. The astronauts photographed terrain and made navigation measurements, becoming the first people to see the farside directly and orbit another celestial body.
References: [1]
Earth above the lunar horizon
During lunar orbit Anders photographed Earth above the grey lunar horizon. Spacecraft motion changed the relative positions of the horizon and planet, producing the colour image known as Earthrise.
Photographs and television broadcasts brought the journey to people on the ground. From lunar orbit the crew described the terrain and showed Earth as a complete distant world.
References: [1]
Returning after ten revolutions
After the lunar-orbit programme, the service-module engine fired again to send the spacecraft toward Earth. Apollo 8 re-entered and splashed down in the Pacific on December 27, where the crew was recovered.
The mission report documented launch, lunar orbit, navigation and return. The flight demonstrated crewed travel to the Moon, orbital operations and return, providing experience for later missions carrying a lunar module.
References: [1]