How do you handle an injured yearling?

Can't give you a proper answer. It all depends on how much handing the yearling has had before the injury and how bad the injury is. You haven't said if it's a joint injury or a flesh wound... As always with horses, you must be calm and quiet but persistent. Reassure the horse and keep it calm, as they can be so quick to get a fright at nothing and injure themselves further when at a young age ...