Polarized and unpolarized neutron scattering techniques along with x-ray diffraction have been used to study the magnetic and structural properties of a single crystal of Nd2CuO4. Long-range magnetic order of the Cu moments develops at TN=245 K, with a simple antiferromagnetic configuration of spins as found in La2NiO4, while the spin directions may be either collinear or noncollinear. Additional abrupt transitions are observed at 75 and 30 K, in which spin reorientations take place. Bragg peaks associated with the crystal structure are found at the same positions as the magnetic Bragg peaks, and indicate that a small distortion of the basic tetragonal structure has occurred above 300 K. At low temperatures the Nd moments also order antiferromagnetically (TN=1.5 K), while an additional transition of a continuous nature is observed at 150 mK.