Cas12a (also called Cpf1) is a representative type V-A CRISPR effector RNA-guided DNA endonuclease, which provides an alternative to type II CRISPR-Cas9 for genome editing. Previous studies have revealed that Cas12a has unique features distinct from Cas9, but the detailed mechanisms of target searching and DNA cleavage by Cas12a are still unclear. Here, we directly observe this entire process by using single-molecule fluorescence assays to study Cas12a from Acidaminococcus sp. (AsCas12a). We determine that AsCas12a ribonucleoproteins search for their on-target site by a one-dimensional diffusion along elongated DNA molecules and induce cleavage in the two DNA strands in a well-defined order, beginning with the non-target strand. Furthermore, the protospacer-adjacent motif (PAM) for AsCas12a makes only a limited contribution of DNA unwinding during R-loop formation and shows a negligible role in the process of DNA cleavage, in contrast to the Cas9 PAM.