SPIDERS: the spectroscopic follow-up of X-ray selected clusters of
  galaxies in SDSS-IV
  SPIDERS (The SPectroscopic IDentification of eROSITA Sources) is a program
dedicated to the homogeneous and complete spectroscopic follow-up of X-ray AGN
and galaxy clusters over a large area ($\sim$7500 deg$^2$) of the extragalactic
sky. SPIDERS is part of the SDSS-IV project, together with the Extended Baryon
Oscillation Spectroscopic Survey (eBOSS) and the Time-Domain Spectroscopic
Survey (TDSS). This paper describes the largest project within SPIDERS before
the launch of eROSITA: an optical spectroscopic survey of X-ray selected,
massive ($\sim 10^{14}$ to $10^{15}~M_{\odot}$) galaxy clusters discovered in
ROSAT and XMM-Newton imaging. The immediate aim is to determine precise
($\Delta_z \sim 0.001$) redshifts for 4,000-5,000 of these systems out to $z
\sim 0.6$. 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.
