A theoretical description of electron spin orientation and detection by short optical pulses is proposed for ensembles of singly charged semiconductor nanocrystals. The complex structure of the valence band in spherical nanocrystals is taken into account. We demonstrate that the direction of electron spin injected by the pump pulse depends on both the pump pulse helicity and the pump pulse power. It is shown that a train of optical pulses can lead to the complete orientation of the resident electron spin. The microscopic theory of the spin Faraday, Kerr and ellipticity effects is developed and the spectral sensitivity of these signals is discussed. We show that under periodic pumping pronounced mode-locking of electron spins takes place and manifests itself as significant spin signals at negative delays between pump and probe pulses.