The total and polarized radio continuum emission of IC 342 was observed in four wavelength bands with the Effelsberg and VLA telescopes. The frequency dependence of the radial scalelength of synchrotron emission indicates energy-dependent propagation of the cosmic-ray electrons, probably via the streaming instability. The equipartition strength of the total magnetic field is typically 15 muG, that of the ordered field 5 muG. Faraday rotation of the polarization angles reveals an underlying regular field of only about 0.5 muG strength with a large-scale axisymmetric spiral pattern, signature of a mean-field dynamo, and an about 10x stronger field that fluctuates on scales of a few 100 pc. The magnetic field around the bar in the central region of IC 342 resembles that of large barred galaxies; its regular spiral field is directed outwards, opposite to that in the disk. The polarized emission in the disk is concentrated in: (1) a narrow arm of about 300 pc width, displaced inwards with respect to the eastern arm by about 200 pc, indicating magnetic fields compressed by a density wave; (2) a broad arm of 300-500 pc width around the northern arm with systematic variations in polarized emission, polarization angles, and Faraday rotation measures on a scale of about 2 kpc, indicative of a helically twisted flux tube generated by the Parker instability; (3) a rudimentary magnetic arm in an interarm region in the north-west; (4) several broad spiral arms in the outer galaxy, related to spiral arms in the total neutral gas; (5) short features in the outer south-western galaxy, probably distorted by tidal interaction. - The generation and development of magnetic arms by a mean-field dynamo probably need a spiral pattern that is stable over a few galactic rotation periods. The dynamo in IC 342 is slow and weak, probably disturbed by the bar, tidal interaction, or a transient spiral pattern.