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We introduce the DESI LOW-ZSecondary Target Survey, which combines the wide-area capabilities of the Dark Energy Spectroscopic Instrument (DESI) with an efficient, low-redshift target selection method. Our selection consists of a set of color and surface brightness cuts, combined with modern machine-learning methods, to target low-redshift dwarf galaxies (z< 0.03) between 19 <r< 21 with high completeness. We employ a convolutional neural network (CNN) to select high-priority targets. The LOW-Zsurvey has already obtained over 22,000 redshifts of dwarf galaxies (M_*< 10⁹M_⊙), comparable to the number of dwarf galaxies discovered in the Sloan Digital Sky Survey DR8 and GAMA. As a spare fiber survey, LOW-Zcurrently receives fiber allocation for just ∼50% of its targets. However, we estimate that our selection is highly complete: for galaxies atz< 0.03 within our magnitude limits, we achieve better than 95% completeness with ∼1% efficiency using catalog-level photometric cuts. We also demonstrate that our CNN selectionsz< 0.03 galaxies from the photometric cuts subsample at least 10 times more efficiently while maintaining high completeness. The full 5 yr DESI program will expand the LOW-Zsample, densely mapping the low-redshift Universe, providing an unprecedented sample of dwarf galaxies, and providing critical information about how to pursue effective and efficient low-redshift surveys.