The three-dimensional structure of drift-wave turbulence and turbulent transport is investigated in plasmas of the stellarator experiment TJ-K. By means of two poloidal Langmuir probe arrays placed at different toroidal positions, density and potential fluctuations are recorded simultaneously at 128 positions on a single flux surface. From these data, the spatial drift-wave turbulence pattern including perpendicular and parallel structure sizes are obtained using a cross-correlation technique. A comparison with the magnetic field structure indicates an initially perfect alignment of turbulent structures with magnetic field lines. Passing over regions with different field-line pitches according to the local variation of the rotational transform, however, results in a measured displacement of turbulent structures with respect to the field lines during their radial propagation. A reduction in the perpendicular correlation lengths in regions of high absolute values of local magnetic shear is found. Prominent and poloidally narrow turbulent transport maxima are measured at different toroidal positions. They are connected by the magnetic field lines and located in regions of negative normal curvature. The poloidal propagation pattern of turbulent structures and the exact position of the transport maximum depend on the magnetic field direction.