The lunar Askaryan technique, which involves searching for Askaryan radio pulses from particle cascades in the outer layers of the Moon, is a method for using the lunar surface as an extremely large detector of ultra-high-energy particles. The high time resolution required to detect these pulses, which have a duration of around a nanosecond, puts this technique in a regime quite different from other forms of radio astronomy, with a unique set of associated technical challenges which have been addressed in a series of experiments by various groups. Implementing the methods and techniques developed by these groups for detecting lunar Askaryan pulses will be important for a future experiment with the Square Kilometre Array (SKA), which is expected to have sufficient sensitivity to allow the first positive detection using this technique. Key issues include correction for ionospheric dispersion, beamforming, efficient triggering, and the exclusion of spurious events from radio-frequency interference. We review the progress in each of these areas, and consider the further progress expected for future application with the SKA.