The X-SHOOTER Lyman α survey at z = 2 (XLS-z2) I: What makes a galaxy a Lyman α emitter? We present the first results from the X-SHOOTER Lyman α survey at z = 2 (XLS-z2). XLS-z2 is a deep spectroscopic survey of 35 Lyman α emitters (LAEs) utilizing ≈90 h of exposure time with Very Large Telescope/X-SHOOTER and covers rest-frame Ly α to H α emission with R ≈ 4000. We present the sample selection, the observations, and the data reduction. Systemic redshifts are measured from rest-frame optical lines for 33/35 sources. In the stacked spectrum, our LAEs are characterized by an interstellar medium with little dust, a low metallicity, and a high ionization state. The ionizing sources are young hot stars that power strong emission lines in the optical and high-ionization lines in the ultraviolet (UV). The LAEs exhibit clumpy UV morphologies and have outflowing kinematics with blueshifted Si II absorption, a broad [O III] component, and a red-skewed Ly α line. Typically, 30 per cent of the Ly α photons escape, of which one quarter on the blue side of the systemic velocity. A fraction of Ly α photons escape directly at the systemic suggesting clear channels enabling an ≈10 per cent escape of ionizing photons, consistent with an inference based on Mg II. A combination of a low effective H I column density, a low dust content, and young starburst determines whether a star-forming galaxy is observed as an LAE. The first is possibly related to outflows and/or a fortunate viewing angle, while we find that the latter two in LAEs are typical for their stellar mass of 109 M⊙. 505 1 1382-1412 1382-1412 Oxford University Press