The main goal of this study is to carry out a spatially resolved investigation of the warm interstellar medium (ISM) in the extremely metal-poor Blue Compact Dwarf (BCD) galaxy HS 2236+1344. Special emphasis is laid on the analysis of the spatial distribution of chemical abundances, emission-line ratios and kinematics of the ISM, and to the recent star-forming activity in this galaxy. This study is based on optical integral field unit spectroscopy data from Gemini Multi-Object Spectrograph at the Gemini North telescope and archival Sloan Digital Sky Survey images. The data were obtained in two different positions across the galaxy, obtaining a total 4 arcsec X 8 arcsec field which encompasses most of its ISM. Emission-line maps and broad-band images obtained in this study indicate that HS 2236+1344 hosts three Giant HII regions. Our data also reveal some faint curved features in the BCD periphery that might be due to tidal perturbations or expanding ionized-gas shells. The ISM velocity field shows systematic gradients along the major axis of the BCD, with its south-eastern and north-western half differing by ~80 km/s in their recessional velocity. The Ha and Hb equivalent width distribution in the central part of HS 2236+1344 is consistent with a very young (~3 Myr) burst. Our surface photometry analysis indicates that the ongoing starburst provides ~50% of the total optical emission, similar to other BCDs. It also reveals an underlying lower-surface brightness component with moderately red colors, which suggest that the galaxy has undergone previous star formation. We derive an integrated oxygen abundance of 12+log(O/H)=7.53\pm0.06 and a nitrogen-to-oxygen ratio of log(N/O)=-1.57\pm0.19. Our results are consistent, within the uncertainties, with a homogeneous distribution of oxygen and nitrogen within the ISM of the galaxy. (abridged)