We present a new study on the interaction of the DNA molecule with the surfactant dodecyltrimethylammonium bromide (DTAB), performed mainly with optical tweezers. Single-molecule force spectroscopy experiments performed in the low-force entropic regime allowed a robust characterization of the DNA-DTAB interaction, unveiling how the surfactant changes the mechanical properties of the biopolymer, the binding parameters, and the competition of the two mechanisms involved in the interaction: electrostatic attraction between the cationic surfactant heads and the negative phosphate backbone of the DNA and hydrophobic interactions between the tails of the bound DTAB molecules, which can result in DNA compaction in solution depending on the quantity of bound surfactant. Finally, force clamp experiments with magnetic tweezers and gel electrophoresis assays confirm that DTAB compacts DNA depending not only on the surfactant concentration but also on the conformation of the biopolymer in solution. The present study provides new insights on general aspects of the DNA-surfactant complexes formation, contributing to the fundamental knowledge of the physics of such interactions.