Context. The Apache Point Observatory Galactic Evolution Experiment (APOGEE) features the first multi-object high-resolution fiber spectrograph in the near-infrared ever built, thus making the survey unique in its capabilities: APOGEE is able to peer through the dust that obscures stars in the Galactic disc and bulge in the optical wavelength range. Here we explore the APOGEE data included as part of the Sloan Digital Sky Survey's 10th data release (SDSS DR10). Aims: The goal of this paper is to a) investigate the chemo-kinematic properties of the Milky Way disc by exploring the first year of APOGEE data; and b) to compare our results to smaller optical high-resolution samples in the literature, as well as results from lower resolution surveys such as the Geneva-Copenhagen Survey (GCS) and the RAdial Velocity Experiment (RAVE). Methods: We select a high-quality (HQ) sample in terms of chemistry (amounting to around 20 000 stars) and, after computing distances and orbital parameters for this sample, we employ a number of useful subsets to formulate constraints on Galactic chemical and chemodynamical evolution processes in the solar neighbourhood and beyond (e.g., metallicity distributions - MDFs, [α/Fe] vs. [Fe/H] diagrams, and abundance gradients). Results: Our red giant sample spans distances as large as 10 kpc from the Sun. Given our chemical quality requirements, most of the stars are located between 1 and 6 kpc from the Sun, increasing by at least a factor of eight the studied volume with respect to the most recent chemodynamical studies based on the two largest samples obtained from RAVE and the Sloan Extension for Galactic Understanding and Exploration (SEGUE). We find remarkable agreement between the MDF of the recently published local (d < 100 pc) high-resolution high-S/N HARPS sample and our local HQ sample (d < 1 kpc). The local MDF peaks slightly below solar metallicity, and exhibits an extended tail towards [Fe/H]= -1, whereas a sharper cutoff is seen at larger metallicities (the APOGEE sample shows a slight overabundance of stars with metallicities larger than ≃+0.3 with respect to the HARPS sample). Both samples also compare extremely well in an [α/Fe] vs. [Fe/H] diagram. The APOGEE data also confirm the existence of a gap in the abundance diagram. When expanding our sample to cover three different Galactocentric distance bins (inner disc, solar vicinity and outer disc), we find the high-[α/Fe] stars to be rare towards the outer zones (implying a shorter scale-length of the thick disc with respect to the thin disc), as previously suggested in the literature. Finally, we measure the gradients in [Fe/H] and [α/Fe], and their respective MDFs, over a range of 6 < R < 11 kpc in Galactocentric distance, and a 0 < z < 3 kpc range of distance from the Galactic plane. We find a good agreement with the gradients traced by the GCS and RAVE dwarf samples. For stars with 1.5 < z < 3 kpc (not present in the previous samples), we find a positive metallicity gradient and a negative gradient in [α/Fe]. Appendix A is available in electronic form at http://www.aanda.org