Bequeathing

The Keyblade Inheritance Ceremony is a trial in which a certain Keyblade master chooses a child or an adolescent to inherit the Keyblade. If the Keyblade also chooses the host, then the host may summon his or her own Keyblade at will. This was first seen in Kingdom Hearts Birth by Sleep between Terra and Riku, as well as between Aqua and Kairi.

Procedure
A Keyblade Inheritance Ceremony may be either intentional or accidental. To pass down the Keyblade intentionally, a Keyblade master must choose a successor. All the master must do is test the one they have chosen's strength by allowing him or her to hold their Keyblade. If the Keyblade also approves of the succession, it will emit a brief glow of light.

The Keyblade is accidentally inherited when one of a strong heart and will makes contact with it. If the Keyblade glows the same way as when passed down intentionally, it can be safely assumed that this person can now summon the Keyblade willingly.

Prominent Keyblade wielders to practice both cases of the Keyblade Inheritance Ceremony are Aqua and Terra. It should be noted that a chosen Keyblade wielder is capable of seeing the door to the heart of a world, as Riku saw in the flashbacks in Kingdom Hearts.

Aqua's Scenario
The Keyblade Inheritance Ceremony is unintentionally performed when Aqua visits Radiant Garden and comes across a young Kairi, who is being attacked by a swarm of Floods. Aqua's Keyblade glows when Kairi runs to hide behind Aqua out of fear, implying she gains the ability to summon Keyblade at this point.

Terra's Scenario
The Keyblade Inheritance Ceremony is intentionally and correctly performed by Terra when he meets a young Riku on the Destiny Islands. Seeing himself through the boy, Terra proceeded to select Riku as his successor.

Trivia

 * It was revealed in Kingdom Hearts Birth by Sleep that Sora was not originally the Keyblade's chosen wielder. Terra had specifically chosen Riku to wield the blade during their encounter on Destiny Islands. Due to Riku's descent into darkness in Kingdom Hearts, however, the Keyblade was led to choose Sora, as Ventus's heart resided within the boy.
 * Aqua is currently known to choose at least two people to be Keyblade wielders, having unintentionally selected both Kairi and Sora. The Kingdom Hearts Birth by Sleep Ultimania reveals that Aqua was going to let Sora inherit the Keyblade, though she sensed Riku had already been selected. This reminded her of the future fights she was to engage Terra in, Aqua withdrawing and instead asking Sora to save Riku if he were to fall into darkness.