In the Felsenkeller shallow-underground site, protected from cosmic muons by a 45 m thick rock overburden, a research laboratory including a 5 MV Pelletron ion accelerator and a number of radioactivity-measurement setups is located. The laboratory and its installations are described in detail. The background radiation has been studied, finding suppression factors of 40 for cosmic-ray muons, 200 for ambient neutrons, and 100 for the background in germanium $γ$-ray detectors. Using an additional active muon veto, typically the background is just twice as high as in very deep underground laboratories. The properties of the accelerator including its external and internal ion sources and beam line are given. For the radioactivity counting setup, detection limits in the 10$^{-4}$ Bq range have been obtained. Practical aspects for the usage of the laboratory by outside scientific users are discussed.