A combined experimental and theoretical study of the layered antiferromagnetic compound ${\mathrm{DyRh}}_{2}{\mathrm{Si}}_{2}$ in the ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type structure is presented. The heat capacity shows two transitions upon cooling: The first one at the N\'eel temperature ${T}_{\mathrm{N}}=55\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and a second one at ${T}_{\mathrm{N}2}=12\phantom{\rule{4pt}{0ex}}\mathrm{K}$. Using magnetization measurements, we study the canting process of the Dy moments upon changing the temperature and can assign ${T}_{\mathrm{N}2}$ to the onset of the canting of the magnetic moments towards the [100] direction away from the $c$ axis. Furthermore, we found that the field dependence of the magnetization is highly anisotropic and shows a two-step process for $H\ensuremath{\parallel}001$. We used a mean-field model to determine the crystalline electric field as well as the exchange interaction parameters. Our magnetization data together with the calculations reveal a moment orientation close to the [101] direction in the tetragonal structure at low temperatures and fields. Applying photoemission electron microscopy, we explore the (001) surface of the cleaved ${\mathrm{DyRh}}_{2}{\mathrm{Si}}_{2}$ single crystal and visualize Si- and Dy-terminated surfaces. Our results indicate that the Si-Rh-Si surface protects the deeper lying magnetically active Dy layers and is thus attractive for investigation of magnetic domains and their properties in the large family of ${\mathrm{LnT}}_{2}{\mathrm{Si}}_{2}$ materials.