How to distinguish P, S, Love, and Rayleigh waves in a seismogram?
There are two important ways to recognize different types of waves in seismic records:


Their velocity. These waves travel at different speeds: P-waves are fastest, then S-waves, then Love waves, then Rayleigh. Since seismic recordings are measures of earth displacement, particle velocity, or water pressure over elapsed time, this means the waves show up at different times in the record. If we know or guess their velocities, then we can model the arrival times at various stations and try to recognize the different wavefronts. Here's one example of a shot record (distance x on the horizontal axis, time t on the vertical) where you can see reflected P-waves and Rayleigh waves: the slope of the arrivals is a function of wave speed. Once we can discriminate them in some domain (commonly t–x, f–x, or tau–p), we can design filters that exploit this fact.
Their mode of oscillation. The waves are distinguished by different types of particple motion. For example, P-waves are longitudinal, S-waves are transverse, Rayleigh waves are circular. So if we have a sensor that can detect particle motion in three dimensions, we can recognize waveforms that way. In the oil &amp; gas industry, where seismic reflection data is an important tool, so-called multi-component (or three-component, or 3C) sensors are now widespread; here's one example. I'm afraid it's beyond me, but I know one of the methods they use to unpack the different waveform polarizations is singular value decomposition. 


Reconciling P- and S-wave reflections is one of the great problems in reflection seismology today. Everything is made more complicated by the fact that these waves can convert from one to the other. For example, when P-waves reflect from an elastic interface, like rock broundaries, some energy is converted into S-waves. Furthermore, some recording equipment is more sensitive to vertical ground motion than to horizontal (e.g. single component geophones), so our records are often strongly filtered. The result is that unpeeling multiple wave types is not easy.