DNA supercoiling, where the DNA strand forms a writhe to relieve torsional stress, plays a vital role in packaging the genetic material in cells. Experiment, simulation, and theory have all demonstrated how supercoiling emerges due to the over- or underwinding of the DNA strand. Nucleoid-associated proteins (NAPs) help structure DNA in prokaryotes, yet the role that they play in the supercoiling process has not been as thoroughly investigated. We develop a coarse-grained simulation to model DNA supercoiling in the presence of proteins, providing a rigorous physical understanding of how NAPs affect supercoiling behavior. Specifically, we demonstrate how the force and torque necessary to form supercoils are affected by the presence of NAPs. NAPs that bend DNA stabilize the supercoil, thus shifting the transition between extended and supercoiled DNAs. We develop a theory to explain how NAP binding affects DNA supercoiling. This provides insight into how NAPs modulate DNA compaction via a combination of supercoiling and local protein-dependent deformations.