It can take anywhere from 5-15 years to design and build a rocket. If it is a new rocket it will usually take a long time. The rockets that were used to go to the Moon in the 1960’s, called the Saturn-5, took about 5 years from design to launch. But at the time, they had lots of money and pressure to finish so things happened a little faster.
Once a rocket is launched it will take about 3 days to get to the Moon and then you can spend a few days there taking pictures and getting samples, before returning home again on another 3 day journey.
The mission doesn’t really take very long but there are many years of hard work that goes into the mission beforehand!