That's an excellent question. Strictly speaking, there is no reason why a spacecraft must orbit the earth before going to the moon. But in practice, this was often done for the Apollo missions. Apollo 11 circled the earth one and a half times. The Apollo rockets were built in stages, with one stage getting the rocket into orbit, and the next stage getting it from earth orbit to the moon. (A third stage was used to come back).

Technically no, it does not. But practically, that is the best way to get the job done. In order to leave the earth’s gravitational tug, an object needs to attain escape velocity which from earth is 11.2 km/s. The usual pattern is to launch into low earth orbit at speed of 8 km/s, check all the systems and do a burn and change the trajectory. But this is not required per se.

A rocket ship does not have to orbit the Earth in order to get to moon. In fact, a ship whose destination in the Moon should not waste any time or fuel orbiting the earth. To get to the moon, a rocket ship must travel fast enough break free of the Earth's orbit, or gravitational pull. This velocity is almost 7 miles per second (over 25,000 miles per hour!) at the surface of the Earth and a little under 4.5 miles per second (over 15,800 miles per hour!). Remember that the closer you are to something with mass, the stronger the gravitational pull. Thus, the farther you are from the Earth, the smaller the escape velocity is.

While a rocket ship can try straight-shooting to where the Moon will be, another approach has been used called a trans-lunar injection (see a picture here: trans-lunar injection). This approach involves burning some fuel to maneuver the rocket ship into an orbit around the Earth and then burning the rest of the fuel and escaping the Earth once the rocket ship has positioned itself to reach the moon.

In short, a rocket ship doesn't have to orbit the Earth to get to the Moon, but it can be more practical to make a pit-stop above the Earth before committing to the whole she-bang!