Interactions of 209-GeV muons within an instrumented magnetized-steel calorimeter have produced 4374 +- 87 ..mu../sup +/..mu../sup -/ pairs from J/psi decay, corresponding to the cross section sigma(..mu..N ..-->.. ..mu.. psi X) = 0.64 +- 0.10 nb. These interactions are classified as either elastic (sigma = 0.36 +- 0.07 nb) or inelastic (sigma = 0.28 +- 0.06 nb) based primarily on the calorimetric determination of E/sub X/. The cross section for elastic psi production by virtual photons, sigma/sub eff/(..gamma../sub V/N), rises with energy nu as log nu. Its dependence on Q/sup 2/ fits the vector-meson dominance form P(..lambda..) = (1 + Q/sup 2//..lambda../sup 2/)/sup -2/, with ..lambda.. = (2.0 - 2.4) +- 0.15 GeV, where the spread in values arises from considering the possibility of a Q/sup 2/ dependence in the decay angular distribution W (theta,phi) and in the nuclear shadowing factor. We find that W(theta,phi) is consistent with the form expected if the reaction ..gamma../sub V/N ..-->.. psiN conserves helicity in the s channel through natural-parity exchange in the t channel. After correction for nuclear effects, d sigma/sub eff//dt is described by the sum of two exponential terms in t, with average t slope b = 2.56 (+0.35 or - 0.32). The photon-gluon fusion (..gamma..g ..-->.. psi) perturbative quantum chromodynamic model for psi production provides an excellent description of the nu dependence of sigma/sub eff/, but cannot simultaneously explain the observed cross section and value of ..lambda... The differential cross section d/sup 2/sigma/sub eff//dzdp/sub perpindicular//sup 2/ for inelastically produced psi's rises approximately linearly with elasticity z identical with E/sub psi//nu. The p/sub perpendicular//sup 2/ dependence is flatter than that of d sigma/dt for elastic events, with average p/sub perpendicular//sup 2/ slope b = 1.46 +- 0.10. The Q/sup 2/ dependence of sigma/sub eff/ is that of P(..lambda..) with ..lambda.. = 3.0 +- 0.2 GeV, and the nu dependence is similar to that observed for elastic production. 101 references, 33 figures, 20 tables.