The ancient Greeks measured the Moon's distance using the size of the Earth's umbral shadow as revealed by the Moon going through it during a total (or deep partial) lunar eclipse.  They knew but could not do, a measurement of lunar parallax, the shift in the sky the Moon would make when seen from two very far away places.   Today we can do both and compare the results.  

The Shadow technique can be done anyplace where the Moon can be watched through the beginning partial, total, and end partial phases of the eclipse.  It can be recorded by drawing or photography.

The Parallax technique is done with two observers sufficiently far apart (we estimate at least 2000 miles (3200 kilometers).  The Moon must be recorded with photographs taken at the exact same time, with a field of view wide enough (4-8 degrees) such that the neighboring stars can be recorded at the same time on both photographs.  Overlaying the photographs, a comparison will show the shift of the stars (or Moon) as seen from the two places.  The larger the shift, the closer the Moon. See the photo below of the shift observed during the June 2011 total lunar eclipse. 

As an example, the following map shows a large area (in pink tones) that can use the umbral, Shadow-cross-section technique, and the striped zones that form the farthest places where the lunar parallax can be accomplished while still being dark enough to show stars (base map courtesy Jet Propulsion Laboratory).

To do your measuring, in a future total lunar eclipse, choose the link below for the Method (Shadow or Parallax) you plan to use!!

Some General Lunar Eclipse Materials and Information

How to take Lunar Eclipse Photographs--by the three photographers on these Web Pages, in Italy, Turkey and China.

Articles on Lunar Eclipses from The Classroom Astronomer magazine: