Prior to the 20th century, the
best way to determine the distance to the

Moon was to use

parallax.
The Moon's coordinates in the sky are slightly different from different
places on Earth. The Moon forms a skinny triangle with the two locations
on Earth. The small angle is the angular distance between the two measured
lunar positions. Its opposite side is the physical distance between the
two places on Earth. Using

trigonometry, you can thus find the distance to
the Moon.

With the invention of RADAR, more precise determinations of the lunar
distance became possible. Also, thanks to the Apollo
astronauts, there is a large reflector on the Moon's surface, off of which
laser light can be bounced from Earth. By measuring the time the laser
light takes to make the round trip to the moon and back, its instantaneous
distance can be measured to within one inch (!).

Average distance to the moon: 384,400 km.