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-P{e}rez et al., Phys. Rev. Lett. 110, 133003 (2013)]. In this paper we provide further details on 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.