Context: Small-scale magnetic fields play an important role in the structure and the dynamics of the solar atmosphere. Aims: This study aims at revealing the evolution of magnetic fields, together with granular convection in the quiet Sun by means of observations with high spatial, spectral, and temporal resolution and of numerical MHD simulations. Methods: Time sequences from quiet Sun disc centre were obtained with the upgraded “Göttingen” Fabry-Perot spectropolarimeter at the Vacuum Tower Telescope, Observatorio del Teide/Tenerife, in the Fe I 6173 Å line. The data were reconstructed with speckle methods. For comparison with the observations, numerical simulations of granular magnetoconvection were carried out with the MURaM code. The intensities and Stokes vectors emerging from the simulation box were degraded in wavelength, spatial co-ordinates, and noise to the quality of the observations. Results: The noise in the observed magnetograms from the centre-of-gravity method is σ_B≈2 G, yielding a polarimetric sensitivity of 3 × 1015 Mx, at a cadence of 23 s with 0.33 arcsec spatial resolution in a field of view of ˜33 arcsec× 25 arcsec. Many of the observed V profiles in network and internetwork (IN) areas exhibit strong asymmetries that indicate strong magnetoconvection. The temporal evolutions of IN structures and of a bright point (BP), as seen in broadband and line-minimum images, in Dopplergrams, and in magnetograms, are presented. The magnetic field structure in the numerical MHD simulations is even more complex than seen in the observations. Correspondingly, the emergent Stokes profiles are often very abnormal. The degradation yields a reduction of the intrinsic field strength to the “observed” one by a factor 4-5. The spectral resolution of the spectrometer is adequate, yet the limitation in spatial resolution and by noise filtering swamps the details seen in the non-degraded simulations. A BP was not found in the simulations, presumably because BP's are not so common and the simulated box is quiet small: only 6 Mm wide in both horizontal directions. Conclusions: The combination of high-resolution observations with numerical simulation is a highly valuable means for studying small-scale magnetic fields on the Sun. Two-dimensional, low-noise data with spectral resolution as good as achieved here and with spatial resolution of 0.1 arcsec and better are needed to better understand this important part of the solar magnetism. A movie is only available in electronic form at http://www.aanda.org