What are the specific rules and mechanics in Magic: The Gathering that govern the ability to regenerate creatures on the battlefield?

In Magic: The Gathering, the ability to regenerate a creature allows it to avoid destruction once. To regenerate a creature, you pay its regeneration cost when it would be destroyed. This creates a shield that prevents the creature from being destroyed that turn. The creature is tapped and removed from combat, but it remains on the battlefield with all damage removed.