We have recently demonstrated static trapping of ammonia isotopologues in a decelerator that consists of a series of ring-shaped electrodes to which oscillating high voltages are applied [Quintero-Pérez et al., Phys. Rev. Lett. 110, 133003 (2013)]. In this paper we provide further details about this traveling-wave decelerator and present new experimental data that illustrate the control over molecules that it offers. We analyze the performance of our setup under different deceleration conditions and demonstrate phase-space manipulation of the trapped molecular sample.