In Star Wars franchise, AT-AT walker is described as "All-Terrain Armored Transport". Its primary function is to carry and deploy troops.
But how exactly does it deploy troops? Do they jump out using some equipment that slows down descent? Or does it provide ladders, ramps, etc?
Canon answers preferred, but Legends also acceptable,
It depends what source you go with but afaik, an operational deployment method has never been confirmed (or seen) in canon.
A walker's body section can carry 40 fully-armed and battle-ready stormtroopers. To load and disembark troops, the AT-AT kneels by bending its tri-jointed legs and lowering its body to within three meters of the ground. A landing ramp drops from the rear of the vehicle to deploy passengers, in addition, hatches on the flanks are used when docked at Imperial boarding platforms.
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In order to release troops, an AT-AT kneels to within three meters off the ground and lowers a rear assault ramp.
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AT-AT walkers load and drop the troops they carry by "kneeling" to allow the use of a ramp in the main body. In this way, battle-ready Stormtroopers "hit the ground running," weapons drawn, initially shielded from enemy fire by the massive bulk of the walker above and around them. Side-mounted hatches allow personnel to enter or exit the vehicle via the boarding ramps of Imperial landing platforms.
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To deploy its complement of troops, an AT-AT must kneel. With the body still three metres from the ground, ramps are lowered for the 40 troops and four speeder bikes to disembark. It is also possible for the troopers to rappel down drop lines from the AT-AT, though they are very vulnerable doing so.
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ASSAULT CARRIERS
AT-AT walkers can unleash their assault forces in several rapid waves using drop-lines with attached harnesses. Boom racks extend to drop combat troops and equipment over the side. Speeder bikes are deployed using harnesses at front and back.
As to how they load (and unload) the AT-AT when they have access to a military base, this is accomplished using a loading platform.
Others have already cited the Star Wars: Incredible Cross-sections books.
I'm sure this question has been asked before, and there's some descriptions in the novels where they kneel down to unload both the troops and the speeder bikes in the back. From memory this was in Dark Apprentice by Kevin J. Anderson.
The Star Wars: Empire at War games show the unloading of troops: the walker takes a wide stance with the front legs forward and the rear legs backward, and the stormtroopers rappel out of the belly: I seem to remember some criticism of the game that while this deployment method was inspired by Luke using his ascension gun and lightsaber in ESB, it was impractical for the troops to deploy in this way since there's no hatches there (and the area is between the legs, where the motors/actuators are).
The Hasbro 2010 AT-AT toy had the side of the model open up with a platform and hook for figures to rappel down on, although how much this toy represents canonical accuracy is perhaps a different topic.
According the the Star Wars: Incredible Cross-sections book, the AT-AT can
Unleash their assault forces in several waves using drop-lines with attached harnesses. Boom racks extend to drop troops and equipment over the side.
In Return of the Jedi, we also see an AT-AT carrying Luke to the shield generator to meet with Vader, and they disembark from the side.
