The vast collecting area of the Square Kilometre Array (SKA), harnessed by sensitive receivers, flexible digital electronics and increased computational capacity, could permit the most sensitive and exhaustive search for technologically-produced radio emission from advanced extraterrestrial intelligence (SETI) ever performed. For example, SKA1-MID will be capable of detecting a source roughly analogous to terrestrial high-power radars (e.g. air route surveillance or ballistic missile warning radars, EIRP (EIRP = equivalent isotropic radiated power, ~10^17 erg sec^-1) at 10 pc in less than 15 minutes, and with a modest four beam SETI observing system could, in one minute, search every star in the primary beam out to ~100 pc for radio emission comparable to that emitted by the Arecibo Planetary Radar (EIRP ~2 x 10^20 erg sec^-1). The flexibility of the signal detection systems used for SETI searches with the SKA will allow new algorithms to be employed that will provide sensitivity to a much wider variety of signal types than previously searched for. Here we discuss the astrobiological and astrophysical motivations for radio SETI and describe how the technical capabilities of the SKA will explore the radio SETI parameter space. We detail several conceivable SETI experimental programs on all components of SKA1, including commensal, primary-user, targeted and survey programs and project the enhancements to them possible with SKA2. We also discuss target selection criteria for these programs, and in the case of commensal observing, how the varied use cases of other primary observers can be used to full advantage for SETI.