Long-slit spectra of the planetary nebula NGC 6543, obtained at high and moderate spectral and high spatial resolution, are presented. The data allow us to study the spatial and kinematical properties of the various components identified in the nebula in great detail and to establish a spatio-kinematical model which can account for the observed velocity field. The basic structure of the nebula is a geometrically thick expanding ellipsoid, mainly defined by an inner shell and an outer shell. A bright ring defines the equatorial plane of the thick ellipsoid. The equatorial expansion velocity in the thick ellipsoid varies from almost-equal-to 16 km s-1, at its inner shell, up to almost-equal-to 28 km s-1, at its outer shell. The polar expansion velocities exceed the equatorial velocities by a factor of almost-equal-to 1.8. Four pairs of narrow, point-symmetric components have been identified in the object, including the previously known bipolar jet-like features. Each pair of point-symmetric components exhibits a filamentary structure characterized by systematic variations of the position and radial velocity. Three of the pairs are embedded in the outer shell of the thick ellipsoid and participate in its expansion. The fourth pair (the bipolar jet-like features) is neither geometrically nor kinematically related to the thick ellipsoid; it seems to be younger than the other nebular components and to move at a higher velocity. The peculiar spatial and kinematical structure deduced for the point-symmetric components, particularly for the jet-like features, is probably the result of highly collimated bipolar mass ejections from the central star. Moreover, the structure suggests that the ejections have occurred along a precessing bipolar axis and that the precession parameters have changed with time. The observed line ratios suggest that shock excitation seems to exist in some of the point-symmetric components and in the jet-like features. The electron density and estimates of the ionized mass have been derived for the prominent components. Minimum values of the electron density (almost-equal-to 10(3) cm-3) and ionized mass (almost-equal-to 2.5 10(-4) M.) are found in the jet-like features. The results favor the proposition that the central object of NGC 6543 is a binary. In this model, the thick ellipsoid results from the interaction of an energetic stellar wind with material of a circumbinary envelope (dispersed during the AGB phase of the primary) which presents an anisotropic density distribution. The filamentary, point-symmetric components are attributed to highly collimated bipolar ejections from the inner parts of an accretion disk about the compact companion. The particular shape of the ejected components can be explained by precession of that disk.