We present an overview of the Southern-sky MWA Rapid Two-metre (SMART) pulsar survey that exploits the Murchison Widefield Array's large field of view and voltage capture system to survey the sky south of 30 • in declination for pulsars and fast transients in the 140-170 MHz band. The survey is enabled by the advent of the Phase II MWA's compact configuration, which offers an enormous efficiency in beam-forming and processing costs, thereby making an all-sky survey of this magnitude tractable with the MWA. Even with the long dwell times employed for the survey (4800 s), data collection can be completed in <100 hours of telescope time, while still retaining the ability to reach a limiting sensitivity of ∼2-3 mJy (at 150 MHz, near zenith), which is effectively 3-5 times deeper than the previous-generation low-frequency southern-sky pulsar survey, completed in the 1990s. Each observation is processed to generate ∼5000-8000 tied-array beams that tessellate the full ∼610 deg 2 field of view (at 155 MHz), which are then processed to search for pulsars. The voltage-capture recording of the survey also allows a multitude of post hoc processing options including the reprocessing of data for higher time resolution and even exploring image-based techniques for pulsar candidate identification. Due to the substantial computational cost in pulsar searches at low frequencies, the survey data processing is undertaken in multiple passes: in the first pass, a shallow survey is performed, where 10 minutes of each observation is processed, reaching about one-third of the full search sensitivity. Here we present the system overview including details of ongoing processing and initial results. Further details including first pulsar discoveries and a census of low-frequency detections are presented in a companion paper. Future plans include deeper searches to reach the full sensitivity and acceleration searches to target binary and millisecond pulsars. Our simulation analysis forecasts ∼300 new pulsars upon the completion of full processing. The SMART survey will also generate a complete digital record of the low-frequency sky, which will serve as a valuable reference for future pulsar searches planned with the low-frequency Square Kilometre Array.