By using the triangulation method
Laser
The mathematical equation which describes how to measure the distance from Earth to the moon using Earth's diameter as a unit of measure is d = Dcot(p/2)/2 Where d is the distance from Earth to the moon, D is the diameter of the Earth and p is the angle of parallax subtended at moon by the diameter of the Earth.
NASA accurately measured the distance between the Earth and the Moon using laser ranging techniques. By bouncing laser beams off retroreflectors left on the Moon's surface by the Apollo missions, scientists could measure the time it took for the light to travel to the Moon and back. This precise timing, combined with the speed of light, allowed them to calculate the exact distance between the two bodies. The measurements have been refined over the years, providing highly accurate data on the Earth-Moon distance.
The average distance between the Moon and Earth is about 238,855 miles (384,400 kilometers). This distance can vary due to the elliptical shape of the Moon's orbit. Scientists use radar ranging and laser ranging techniques to precisely measure this distance.
Lunar Laser Ranging experiment. See related link.
The easiest way to measure the distance between Earth and the moon is through radar ranging, where radio signals are sent and the time taken for them to bounce back is used to calculate the distance. This method is more accurate and reliable than using visual cues.
The distance to the moon is about 1.3 light seconds or about 0.000000032 light years.
You can determine the distance to the moon using a method known as parallax. First, measure the diameter of the moon and hold the meter stick vertically at arm's length, creating a right triangle with the moon as one vertex. By moving the meter stick to two different positions and measuring the angle subtended by the moon at these positions, you can calculate the distance to the moon using basic trigonometry. The relationship between the diameter of the moon, the angles measured, and the distance will allow you to derive the moon's distance from Earth.
nobody
Laser light.
Put a mirror on the moon and shine a laser on it and time how long it takes for the beam to be reflected back. You know the speed of light so can work out the round trip distance. Apollo astronauts did leave a mirror on the moon. http://www.lpi.usra.edu/lunar/missions/apollo/apollo_11/experiments/lrr/
The average distance between Earth and the Moon is about 384,400 km. One light year is the distance light travels in one year, approximately 9.46 trillion km. So, the smallest distance is from Earth to the Moon.