We present results on the compact steep-spectrum quasar 3C 48 from observations with the VLBA, MERLIN and EVN at multiple radio frequencies. In the 1.5-GHz VLBI images, the radio jet is characterized by a series of bright knots. The active nucleus is embedded in the southernmost VLBI component A, which is further resolved into two sub-components A1 and A2 at 4.8 and 8.3 GHz. A1 shows a flat spectrum and A2 shows a steep spectrum. The most strongly polarized VLBI components are located at component C $sim$0.25 arcsec north of the core. The polarization angles at C show gradual changes across the jet width at all observed frequencies, indicative of a gradient in the emission-weighted intrinsic polarization angle across the jet and possibly a systematic gradient in the rotation measure; moreover, the percentage of polarization increases near the curvature at C, likely consistent with the presence of a local jet-ISM interaction and/or changing magnetic-field directions. The hot spot B shows a higher rotation measure, and has no detected proper motion. These facts provide some evidence for a stationary shock in the vicinity of B. Comparison of the present VLBI observations with those made 8.43 years ago suggests a proper motion of $beta_{app}=3.7pm0.4 c$ for A2 to the north. The apparent superluminal motion suggests that the relativistic jet plasma moves at a velocity of $gtrsim0.96 c$ if the jet is viewed at an inclination angle less than $20degr$. A simple precessing jet model and a hydrodynamical isothermal jet model with helical-mode Kelvin-Helmholtz instabilities are used to fit the oscillatory jet trajectory of 3C 48 defined by the bright knots.
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