A pulsar timing array (PTA) is an initiative to observe, record, and analyze the timing of a set ("array") of pulsars with one or more radio telescopes, aimed at detecting very-long wavelength (light-years) gravitational waves through comparison of the timing of observed pulsar cycles. (The term "array" could be read as meaning the use of multiple telescopes in such an initiative, and may sometime be intended in that way, but as far as I can see, the advantage of multiple telescopes is the practical issues of getting sufficient telescope time and the necessary field of view and perhaps confirming the accuracy of measurement through redundancy. Possibly information on the direction of the GW source can be gleaned.) Data so-collected is termed pulsar timing data.
PTAs constitute galactic-scale detectors, significantly scaled up from LIGO-like ground detectors or LISA-like space detectors. Some PTAs:
The observations look for very long period gravitational waves expected from closely orbiting binary SMBHs, which would presumably be on track to merge, but actual detectable mergers would be sufficiently rare as not to be expected in our lifetime. The gravitational waves make the space between a pulsar and the Earth longer and shorter, so the steady pulses take more and less time to reach Earth. To find these, PTAs look for long-term changes in the timing of pulses received from millisecond pulsars (This type of pulsar is the most consistent, producing fewer their own glitches in the timing than other pulsars). Since such pulsars emit pulses with a consistency comparable to our best (i.e., atomic) clocks, how to time them is a challenge. The timing of pulses and their variations can be gathered by periodic (e.g., monthly) viewing of the pulsars, and the recorded variations over time constitute all the necessary data. The results of many observations is "averaged".
The wave periods would be year-long and more, and the waves move at the speed of light, so for a pulsar some kpc distant, many wave cycles can sit between, Earth and the source, and each such entire wave "cancels", since part of its phase is making the EMR path longer and another part making it shorter. The waves stem directly from the supermassive black hole orbits (in the simplest case, a circular orbit, there is a wave for each half orbit). The timing differences are due to the waves passing the line of sight between the pulsar and the Earth, the waves being transverse meaning distances across the wave direction are shortened and lengthened. Effects at the Earth end should affect the timing of (virtually) every pulsar being viewed, the degree depending upon the direction of the specific pulsar, thus observing a number of pulsars helps. The exact delta in the timing of each depends upon the angle between the wave front and the pulsar's direction from Earth. Effects at the pulsar end may be useful, but require more effort to use: each pulsar would be a different distance from the source, so different waves would be passing over them and the phases won't match. To detect the longest detectable waves, an ongoing change in timing may be all that is observable (the differential of the timing deltas), adding more challenges to sorting out a signal.
Processing includes removing all the other effects on timing, which includes position of the Earth in its orbit, the motion of the Sun, and the effect of planets (e.g., Jupiter is massive enough to effect EMR paths passing close to it), the uncertainties in the equipment, and then distinguishing one or more frequencies (of pulse arrivals, not of EMR wavelength) in the signal, each the result of some binary pair. To that, an "un-blending" of periods of all the waves needs to be accomplished. A particular detected frequency, in phase, showing from all the pulsars would indicate waves passing Earth from a particular source. Getting a direction on the source would require analyzing the affect on different pulsars according to the angle between wavefront and the lines of sight to the pulsars, so the more pulsars being observed, the better. The data from multiple pulsars are also used to refine the precise space/time reference used, somewhat in analogy to the processing done in high-precision astrometric surveys: statistical processing to (in effect) the "minimize the sum of least squares" of apparent divergences, i.e., to identify the most likely time reference based upon all the data. Timing noise (TN), e.g., from instrument limits and from solar system ephemerides must be identified and taken into account.
The PTA effort is also trying to characterize and detect the gravitational wave background (GWB) over this frequency range due to all the producers of such waves throughout the universe.