We present deep long-slit optical spectra for a sample of 36 ultraluminous infrared galaxies (ULIRGs), taken with the William Herschel Telescope on La Palma with the aim of investigating the star formation histories and testing evolutionary scenarios for such objects. Here we present the sample, the analysis techniques and a general overview of the properties of the stellar populations; a more detailed discussion will be presented in a forthcoming paper. Spectral synthesis modelling has been used in order to estimate the ages of the stellar populations found in the diffuse light sampled by the spectra in both the nuclear and extended regions of the target galaxies. We find that adequate fits can be obtained using combinations of young stellar populations (YSPs; tYSP <= 2Gyr), with ages divided into two groups: very young stellar populations (VYSPs; tVYSP <= 100Myr) and intermediate-young stellar populations (IYSPs; 0.1 < tIYSP <= 2Gyr). Our results show that YSPs are present at all locations of the galaxies covered by our slit positions, with the exception of the northern nuclear region of the ULIRG IRAS23327+2913. Furthermore, VYSPs are present in at least 85 per cent of the 133 extraction apertures used for this study, being more significant in the nuclear regions of the galaxies. Old stellar populations (OSPs; tOSP > 2Gyr) do not make a major contribution to the optical light in the majority of the apertures extracted. In fact they are essential for fitting the spectra in only 5 per cent (seven) of the extracted apertures. The estimated total masses for the YSPs (VYSPs + IYSPs) are in the range 0.18 × 1010 <= MYSP <= 50 × 1010Msolar. We have also estimated the bolometric luminosities associated with the stellar populations detected at optical wavelengths, finding that they fall in the range 0.07 × 1012 < Lbol < 2.2 × 1012Lsolar. In addition, we find that reddening is significant at all locations in the galaxies. This result emphasizes the importance of accounting for reddening effects when modelling the stellar populations of star-forming galaxies.