An approach to screening a core hole's potential in solids for purposes such as theoretical near-edge spectrum calculations is developed. In this approach, the core hole's unscreened potential is decomposed into a short-range part and a long-range part. The short-range part is screened using a real-space screening calculation, while the long-range part can be screened using a model dielectric function. Screening of the core hole is computed for 1s holes in LiF, MgO, Si, solid argon, diamond, and two structures of hafnium oxide. Most of the screening results obtained using the approach presented here are compared to similar results obtained using a traditional Fourier-space approach. Because the approach presented here is a real-space approach, it should be very practical for systems with large unit cells.