I would like to calibrate the Heston model and I am wondering which are the most common approaches used in the literature. Any suggestions (references from the main stream literature, notes or presentations) is greatly appreciated.
If you want to calibrate on time series, then you have a 'non linear filtering' problem, since volatility is latent. There have been papers from late 90s/ early 00s that do that: Google for Heston together with Ghysels, Gallant, Renault, Chernov, Tauchen, Pan, Bates, Shephard, MCMC, unscented Kalman filter/ particle filter.
Given the significant complexity though, you should understand your motivation and requirements. Ask yourself why calibrate Heston on time series? Why a more straightforward Garch variant is not sufficient?