In anticipation of the upcoming InSight mission, which is expected to deploy a single seismic station on the Martian surface in November 2018, we describe a methodology that enables locating marsquakes and obtaining information on the interior structure of Mars. The method works sequentially and is illustrated using single representative 3-component seismograms from two separate events: a relatively large teleseismic event (M_w5.1) and a small-to-moderate-sized regional event (M_w3.8). Location and origin time of the event is determined probabilistically from observations of Rayleigh waves and body-wave arrivals. From the recording of surface waves, averaged fundamental-mode group velocity dispersion data can be extracted and, in combination with body-wave arrival picks, inverted for crust and mantle structure. In the absence of Martian seismic data, we performed full waveform computations using a spectral element method (AxiSEM) to compute seismograms down to a period of 1 s. The model (radial profiles of density, P- and S-wave-speed, and attenuation) used for this purpose is constructed on the basis of an average Martian mantle composition and model areotherm using thermodynamic principles, mineral physics data, and viscoelastic modeling. Noise was added to the synthetic seismic data using an up-to-date noise model that considers a whole series of possible noise sources generated in instrument and lander, including wind-, thermal-, and pressure-induced effects and electromagnetic noise. The examples studied here, which are based on the assumption of spherical symmetry, show that we are able to determine epicentral distance and origin time to accuracies of ∼ 0.5-1° and ± 3-6 s, respectively. For the events and the particular noise level chosen, information on Rayleigh-wave group velocity dispersion in the period range ∼ 14-48 s (M_w5.1) and ∼ 14-34 s (M_w3.8) could be determined. Stochastic inversion of dispersion data in combination with body-wave travel time information for interior structure, allows us to constrain mantle velocity structure to an uncertainty of ∼ 5%. Employing the travel times obtained with the initially inverted models, we are able to locate additional body-wave arrivals including depth phases, surface and Moho (multiple) reflections that may otherwise elude visual identification. This expanded data set is reinverted to refine interior structure models and source parameters (epicentral distance and origin time).