PSR J1740-3052 is a young pulsar in orbit around a companion that is most likely a B-type main-sequence star. Since its discovery more than a decade ago, data have been taken at several frequencies with instruments at the Green Bank, Parkes, Lovell, and Westerbork telescopes. We measure scattering timescales in the pulse profiles and dispersion measure changes as a function of binary orbital phase and present evidence that both of these vary as would be expected due to a wind from the companion star. Using pulse arrival times that have been corrected for the observed periodic dispersion measure changes, we find a timing solution spanning 1997 November to 2011 March. This includes measurements of the advance of periastron and the change in the projected semimajor axis of the orbit and sets constraints on the orbital geometry. From these constraints, we estimate that the pulsar received a kick of at least ~50 km/s at birth. A quasi-periodic signal is present in the timing residuals with a period of 2.2 times the binary orbital period. The origin of this signal is unclear.