We provide a comprehensive description of experiment E835 at Fermilab, a high-precision experimental study of charmonium bound states. The c ̄ c states are formed in p ̄ p annihilations of cooled antiprotons stored in the Fermilab Antiproton Accumulator using a dense internal hydrogen gas-jet target. We describe the experimental strategies adopted for detecting the tiny c ̄ c resonant signals in the huge non-resonant hadronic background, and for measuring resonance parameters with high precision.