In order to heal an injury, you must submit a prompt wherein there is a fully trained physician tending to an injury on an injured colonist. 
When a colonist reaches HP of 0, they automatically become Injured and must be healed via this prompt before they can have HP regained in the Hospital.

Restrictions
Injured colonists also must be healed before they can breed.
They also are limited in activities, reducing their number of rolls possible by 2.