We present Hα, [N II] lambda6583, [O III] lambda5007 ground-based images, Hubble Space Telescope (HST) (V band) archival images, VLA-A 3.6 cm continuum data, and high-resolution long-slit spectra of the planetary nebula NGC 6884. The VLA and HST images show an extremely knotty and filamentary nebula with an elliptical central structure also recognizable in Hα and [O III]. The [N II] image is different and is dominated by two bright arclike structures. The image ratio maps indicate a complex ionization structure within the nebula with low-excitation filaments surrounded by high-excitation regions. The spectra make it possible to distinguish three basic structural components in NGC 6884: (1) a compact (3.8"x2.8", P.A.~=32^deg), high-excitation ([N II] lambda6583/Hα<=0.15) ellipsoidal shell seen almost pole-on with polar and equatorial expansion velocities in the Hα line of ~=25 and ~=19 km s^-1, respectively; (2) two point-symmetric, low-excitation ([N II]/Hα~=0.6-1) spirals in which the distance to the central star and the radial velocity exhibit systematic variations; (3) two compact, apparently isolated, low-excitation bipolar knots. All data agree that the spirals represent precessing bipolar jetlike outflows. The observational properties of these precessing outflows can satisfactorily be explained with an approximately constant ejection velocity (~=55 km s^-1) and a large precession angle (2phi~=120^deg). The deduced precession period (~=500x[D(kpc)/2] yr) is the shortest one measured so far in this kind of structure in planetary nebulae. The image ratio maps and the [N II]/Hα intensity ratio suggest shock excitation in the precessing jets. A general discussion of NGC 6884 is presented within the context of planetary nebulae with jetlike components.