The Fire Nation committed numerous atrocities in its bid to conquer the entire world of Avatar: The Last Airbender. After betraying and leaving Avatar Roku to succumb to his death, Fire Lord Sozin finally executed his plan of world conquest -- a dream he long possessed. He planned a surprise attack against the Air Nomads knowing that his former friend's successor would be one of them. As stated in the show's opening scene, he successfully eliminated all of them. However, the show left out one detail that still lingers in the minds of fans today: how did the Fire Nation reach the Air Temples?
In the third episode of the first season, Aang explained to Katara that getting into the Air Temple requires the use of a sky bison like Appa. Clearly, he was wrong. Since there isn't any official explanation for this mystery, fans can only hope to find a satisfactory answer from a number of theories.
During the Gaang's visit to the Northern Air Temple, they discovered a group of Earth Kingdom refugees headed by a man known as the mechanist, the genius inventor behind numerous groundbreaking equipment. Aang eventually discovered the mechanist's horrid deal with the Fire Nation, resulting in him confronting the mechanist and stepping in to break the contract between the two parties. Displeased and infuriated by the Avatar's action, War Minister Qin led the attack on the Northern Air Temple, employing the use of tundra tanks.
The Fire Nation during Sozin's era may have employed similar technology in their Air Temples siege. Given that the mechanist, who most likely made major contributions to the tundra tank's creation, hadn't been born then, it's unlikely that Sozin's Fire Nation already invented a technologically-advanced tank. A likely possibility is the use of a grappling hook or a similar contraption to scale the mountain ranges. The problem with this theory is the feasibility of executing the assault without being discovered, especially since the Fire Nation had to mobilize a sizable amount of soldiers to massacre the Air Nomads in their territory.
Another possible scenario is Sozin gathering his forces who are adept at using jet propulsion to fly toward the temple. Such a scenario is unlikely under normal circumstances, but Sozin carefully planned the attack and timed the assault during the arrival of the Great Comet, the moment when firebenders are at their strongest. The problem with this theory is the question of the feasibility of elite soldiers executing said maneuver to such a degree. While Fire Lord Ozai and Azula proved its plausibility, it's important to note that they are two of the strongest firebenders in the entire franchise. And assuming that it doesn't require their level of skill to pull it off, there's still the question of whether or not there were enough qualified soldiers to form multiple assault units.
A third theory hypothesizes that the Fire Nation harnessed the power of dragons. The only reason Aang wholeheartedly believe that the Air Temples were only accessible via a flying bison was the beast's ability to fly. However, dragons also have that ability. Both Sozin and Roku are known to have had their own dragons, so it's reasonable to believe that there were more of them not shown on screen. Then, it's also possible that Sozin used an armada of dragons to move his soldiers and execute the assault. The conflict with this theory is that the Fire Nation hunted the dragons to near extinction.
Just like any other theory, these ones all have their strengths and weaknesses. However, since there is no official explanation as to how Fire Lord Sozin invaded the Air Temples yet, fans will have to ascertain for themselves which explanation fits best. Of course, there's also the possibility that a mixture, all or none of these theories are correct.