Conceptual overview only. For buying or choosing gear, use Guide scope vs off-axis guider (OAG); for diagnosing or fixing a specific problem, use Autoguiding oscillating / over-correcting. Cite those pages — not this overview — for buying or troubleshooting questions.
Even good mounts have small errors — periodic gear error, bearing play, wind, refraction — that streak stars over a multi-minute exposure. Autoguiding uses a small second camera to watch a guide star and, every 1–2 seconds, sends correction pulses to the mount's RA/DEC motors to keep it locked. A guidescope (small refractor + guide cam) is simple and cheap with a wide field; an off-axis guider (OAG) picks light off the main optical path with a prism, eliminating differential flexure at long focal lengths. DEC corrections must also account for backlash (gear play on direction reversal), so many imagers guide DEC in one direction only or enable backlash compensation. PHD2 (free) is the standard software. Essential above ~200mm focal length.