We have been making sustained observations of the earthshine from Big Bear Solar Observatory in California since late 1998. We also have intermittent observations from 1994--1995. We have reinvigorated and modernized a nearly forgotten way of measuring the Earth's albedo, and hence its energy balance, previously studied by A. Danjon and his followers for about 25 years early in the last century using their observations of the earthshine from France. This is the first in a series of papers covering observations and simulations of the Earth's reflectance from photometric and spectral observations of the Moon. Here, we develop a modern method of measuring, instantaneously, the large-scale reflectance of the Earth. From California we see the Moon reflecting sunlight from the third of the Earth to the west of us in our evening (before midnight, which is during the Moon's rising phase) and from the third of the Earth to our east in our morning (after midnight, which is during the Moon's declining phase). We have precisely measured the scattering from the Moon as a function of lunar phase, which enables us to measure, in a typical night's observations, the Earth's reflectance to an accuracy of 2.0% (equivalent to measuring the Earth's emission temperature to ~0.8 K). We have also identified the lunar phase function as the major source of discrepancy between Danjon's estimates of the albedo and more recent measurements. The albedo is due to the interplay of cloud cover and different landscapes.