We have studied J/ψ production in pp collisions at s = 1.8 TeV with the D detector at Fermilab using μ + μ - data. We have measured the inclusive J/ψ production cross section as a function of J/ψ transverse momentum,p T . For the kinematic range p T > 8 GeV/c and η < 0.6 we obtain σ(pp → J/ψ +X ) Br(J/ψ → μ + μ - ) = 2.08 ± 0.17 (stat) ± 0.46(syst) nb. Using the muon impact parameter we have estimated the fraction of J/ψ mesons coming from B meson decays to bef b = 0.35 ± 0.09(stat) ± 0.10(syst) and inferred the inclusive b production cross section. From the information on the event topology the fraction of nonisolated J/ψ events has been measured to be f n o n i s o l = 0.64 ± 0.08(stat) ± 0.06(syst). We have also obtained the fraction of J/ψ events resulting from radiative decays of χ c states, f χ = 0.32 ± 0.07(stat) ± 0.07(syst). We discuss the implications of our measurements for charmonium production processes.