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The 89 s X-ray pulsar XTE J1906+09 was discovered during Rossi X-Ray Timing Explorer (RXTE) observations of SGR 1900+14 in 1996. Because of monitoring campaigns of SGR 1900+14, XTE J1906+09 was also monitored regularly in 1996 September, 1998 May-June, 1998 August-1999 July, and 2000 March-2001 January. A search for pulsations resulted in detections of only the two previously reported outbursts in 1996 September and 1998 August-September. Pulsed flux upper limits for the rest of the observations show that XTE J1906+09 is a transient X-ray pulsar and likely has a Be star companion. The RXTE all-sky monitor did not reveal XTE J1906+09. Pulse-timing analysis of the second outburst discovered a sinusoidal signature in the pulse frequencies that is likely produced by an orbital periastron passage. Fits to pulse phases using an orbital model and quadratic phase model have chi(exp 2) minima at orbital periods of 26-30 days for fixed mass functions of 5, 10, 15, and 20 solar masses. The pulse shape showed energy- and intensity-dependent variations. Pulse-phase spectroscopy quantified the energy-dependent variations. The phase-averaged spectrum used the pulse minimum spectrum as the background spectrum to eliminate effects from SGR 1900+14 and the Galactic ridge and was well fitted by an absorbed power law with a high-energy cutoff with column density N(sub H) = 6 +/- 1 x 10(exp 22)/sq cm, a photon index of 1.01 +/- 0.08, cutoff energy E(sub cut) = 11 +/- 1 keV, and e-folding energy E(sub fold) = 19 +/- 4 keV. Estimated 2-10 keV peak fluxes, corrected for contributions from the Galactic ridge and SGR 1900+14, are 6 x l0(exp -12) and 1.1 x 10(exp -10) ergs/sq cm/s for the 1996 and 1998 outbursts, respectively. XTE J1906+09 may be part of an unusual class of Be/X-ray binaries that do not lie on the general spin period versus orbital period correlation with the majority of Be/X-ray binaries.