The EFAR project is a study of 736 candidate elliptical galaxies in 84 clusters lying in two regions, toward Hercules-Corona Borealis and Perseus-Pisces-Cetus, at distances cz~6000-15000km/s. In this paper (the first of a series), we present an introduction to the EFAR project and describe in detail the selection of the clusters and galaxies in our sample. Fundamental data for the galaxies and clusters are given, including accurate new positions for each galaxy and redshifts for each cluster. The galaxy selection functions are determined by using diameters measured from Schmidt sky survey images for 2185 galaxies in the cluster fields. Future papers in this series will present the spectroscopic and photometric observations of this sample, investigate the properties of the fundamental plane for elliptical galaxies, and determine the large-scale peculiar velocity fields in these two regions of the universe.