Electron current layers (ECLs) are the sites where magnetic reconnection initiates in a current sheet. Using three-dimensional particle-in-cell simulations, we study the plasma processes that occur in an ECL as it evolves rapidly over a short time scale much shorter than the ion cyclotron period. The processes include its thinning, generation of electrostatic instabilities, trapping and heating of electrons in growing waves, its rebroadening, generation of anomalous resistivity, and eventually the generation of large-amplitude magnetic fluctuations. These fluctuations could be interpreted in terms of electron tearing and/or Weibel instabilities, which are commonly invoked as mechanisms for the magnetic reconnection onset. The widths of the broadened ECL are compared with those measured in the magnetic reconnection experiment, showing excellent agreement.