  We present the method and observations for the measurement of the
Extragalactic Background Light (EBL) utilizing the shadowing effect of a dark
cloud. We measure the surface brightness difference between the opaque cloud
core and its unobscured surroundings. In the difference the large atmospheric
and Zodiacal light components are eliminated and the only remaining foreground
component is the scattered starlight from the cloud itself. Although much
smaller, its separation is the key problem in the method. For its separation we
use spectroscopy. While the scattered starlight has the characteristic
Fraunhofer lines and 400 nm discontinuity the EBL spectrum is smooth and
without these features. Medium resolution spectrophotometry at $\lambda$ = 380
- 580 nm was performed with ${VLT}$/FORS at ESO of the surface brightness in
and around the high-galactic-latitude dark cloud Lynds 1642. Besides the
spectrum for the core with $A_V \ge 15$ mag, further spectra were obtained for
intermediate-opacity cloud positions. They are used as proxy for the spectrum
of the impinging starlight spectrum and facilitate the separation of the
scattered starlight (cf. Paper II, Mattila et al. 2017b). Our spectra reach a
precision of $\sim 0.5$ $10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$\AA$^{-1}$ as
required to measure an EBL intensity in range of $\sim$1 to a few times
$10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$\AA$^{-1}$. Because all surface
brightness components are measured using the same equipment the method does not
require unusually high absolute calibration accuracy, a condition which has
been a problem for some previous EBL projects
