We have mapped the CO, HCO+, CS, and N2H+ emission around a low-luminosity Class 0 source IRAM 04191+1522 in the Taurus molecular cloud using the Berkeley-Illinois-Maryland Association array. A bipolar molecular outflow is seen in CO, HCO+, and CS emission originating from around the IRAM source, while a flattened envelope is seen in N2H+ emission surrounding the waist of the molecular outflow around the IRAM source. Outflow, rotation, and probably infall are seen around the Class 0 source, indicating a complicated context for star formation in the earliest stages. The N2H+ envelope is a thick clumpy torus with a tenuous outer part and a ringlike dense inner edge. The dense inner edge has a mean radius of 10'', or 1400 AU. The outer part of the torus exhibits differential rotation, and the infalling material appears to carry angular momentum inward toward the central source. The region surrounded by the inner edge of the torus may have a solid-body rotation. The envelope may result from the collapse of a rotating, magnetized toroid toward the central source. Outflow motion is seen in the outer part of the inner edge of the torus, probably due to an interaction with the molecular outflow. Two armlike structures are seen extending out from the inner edge in the torus. One of them is clearly seen with the velocity increasing roughly linearly with the distance. The HCO+ emission around the source may trace the central core around the source, showing a velocity structure connecting to that of the outer part of the torus. The molecular outflow is best seen in CO. It is bipolar with both a southwest and a northeast lobe. Two internal structures are seen along the main outflow axis within the lobes: (1) a strong CO emission at ~20'' to the northeast of the IRAM source, likely tracing an internal bow shock driven by a collimated, episodic jet and (2) a linear HCO+ structure of ~50'' length at low blueshifted velocity to the southwest of the IRAM source, requiring some interaction with a jet to be produced. In addition, a dense condensation is also seen in HCO+ and CS to the south of the IRAM source, likely representing a recent strong outflow interaction.