SPIDERS (The SPectroscopic IDentification of eROSITA Sources) is a programme dedicated to the homogeneous and complete spectroscopic follow-up of X-ray active galactic nuclei and galaxy clusters over a large area (similar to 7500 deg(2)) of the extragalactic sky. SPIDERS is part of the Sloan Digital Sky Survey (SDSS)-IV project, together with the Extended Baryon Oscillation Spectroscopic Survey and the Time-Domain Spectroscopic Survey. This paper describes the largest project within SPIDERS before the launch of eROSITA: an optical spectroscopic survey of X-ray-selected, massive (similar to 10(14)-10(15) M-circle dot) galaxy clusters discovered in ROSAT and XMM-Newton imaging. The immediate aim is to determine precise (Delta(z) similar to 0.001) redshifts for 4000-5000 of these systems out to z similar to 0.6. The scientific goal of the program is precision cosmology, using clusters as probes of large-scale structure in the expanding Universe. We present the cluster samples, target selection algorithms and observation strategies. We demonstrate the efficiency of selecting targets using a combination of SDSS imaging data, a robust red-sequence finder and a dedicated prioritization scheme. We describe a set of algorithms and work-flow developed to collate spectra and assign cluster membership, and to deliver catalogues of spectroscopically confirmed clusters. We discuss the relevance of line-of-sight velocity dispersion estimators for the richer systems. We illustrate our techniques by constructing a catalogue of 230 spectroscopically validated clusters (0.031 < z < 0.658), found in pilot observations. We discuss two potential science applications of the SPIDERS sample: the study of the X-ray luminosity-velocity dispersion (L-X-sigma) relation and the building of stacked phase-space diagrams.