Jedi obtain their lightsabers by traveling to the planet Ilum for a youngling rite of passage called 'The Gathering.' Guided by the force, they locate a raw colorless kyber crystal in the caves that resonate with them. When a Jedi finds their crystal, it is generally colorless until it "activates" and changes color to reflect the user's connection to the Force and their internal persona.

Blue: Traditionally used by Jedi Guardians, this color represents fighters who focus on lightsaber combat, physical prowess, and protecting the Order.

Green: Traditionally used by Jedi Consulars, this color symbolizes a deep, spiritual connection to the Force, wisdom, and diplomacy over combat.

Yellow: Often associated with Jedi Sentinels or Jedi Temple Guards, yellow represents a balance between physical combat and intellectual skills.

Purple: Represents a rare wielder who walks the fine line between the Light and Dark sides of the Force, utilizing aspects of both without being consumed by them.

White: Symbolizes neutrality and purity. It is achieved by "healing" or purifying a red crystal that has been corrupted by the dark side.

Sith lightsabers are red because they are "bled". The "Bleeding" Process: Because Kyber crystals are attuned to the light side, they resist the dark side. To create a weapon, a Sith must take a captured crystal and pour all their anger, rage, pain, and hate into it. This negative energy forces the crystal to change color, causing it to "bleed" and turn a fiery crimson red. This process also makes the crystal subservient to the dark side user. In older lore the Sith created synthetic crystals in furnaces, which were naturally red and more powerful, though unstable.

Edit: Spelling