We describe the 2dF Galaxy Redshift Survey (2dFGRS) and the current status of the observations. In this exploratory paper, we apply a principal component analysis to a preliminary sample of 5869 galaxy spectra and use the two most significant components to split the sample into five spectral classes. These classes are defined by considering visual classifications of a subset of the 2dF spectra, and also by comparison with high-quality spectra of local galaxies. We calculate a luminosity function for each of the different classes and find that later-type galaxies have a fainter characteristic magnitude, and a steeper faint-end slope. For the whole sample we find M* = -19.7 (for Ω = 1, H0 = 100 km s-1 Mpc-1), α = -1.3, φ* = 0.017. For class 1 ('early-type') we find M* = -19.6, α = -0.7, while for class 5 ('late-type') we find M* = -19.0, α = -1.7. The derived 2dF luminosity functions agree well with other recent luminosity function estimates.