After saying "Watch the power of Aura!" (波動の力をみよ！, Witness the power of the wave guide!) in Brawl, or "Max Aura!" (はどう最大!, Wave-Guide Maximum!) in Ultimate, Lucario flies to the top of the screen in the center of the stage and then shoots a powerful beam attack which can be angled left or right.
"Aura Storm" is not an actual attack in the Pokémon series. However, it resembles Hyper Beam, a special Normal-type attack that, while very powerful, forces the user to waste a turn recharging after a successful use. Most fully evolved Pokémon can learn this move, including Deoxys and Lucario itself.
Any character in the way of the beam takes minor damage if they are farther away, but a lot more when up close. It also spikes with a set but high knockback when used up close. Lucario then holds its hands above its head as it readies the attack, before launching a large beam of Aura downwards. The attack hits multiple times before a big finisher that has significant KO power. Lucario can angle the beam sideways during both the windup and the launch, which is a decent way to catch unhit enemies, although angling can also free trapped targets (which otherwise cannot escape). The move is one of the more difficult Final Smashes to use effectively, as flying or floating characters, or characters with great vertical recovery like Luigi and Meta Knight may be able to easily outrun the beam, while other characters can manage to dodge most of the attack depending on the stage.
As Aura Storm is an Aura-based attack, it has greater power and knockback if Lucario has taken a good amount of damage. With Lucario at 170%, it deals 78% damage and is a one-hit KO against most characters. If Lucario activates on a character, the takeoff hit will deal 28%, making it a maximum of 105% damage and an almost guaranteed one-hit KO.
In Super Smash Bros. Ultimate, while the attack is mostly the same, Lucario will now shout "Max Aura!" (はどう最大!, Wave-Guide Maximum!), Mega Evolve into Mega Lucario, and unleash a wider beam of Aura downwards, making it harder to air dodge through it. Additionally, all opponents are slowed down in the time between Lucario initiating the Final Smash and releasing the beam, making it easier to hit with.