The training session asked workers how they would respond to troubled people — a drug user, an abuse victim or someone with bipolar disorder — that they might encounter on the job. They weren’t doctors or therapists, and their employer, a wide-ranging youth outreach organization called The Door, isn’t only a counseling center. But mental health how-tos are part of everyone’s training, whether they’re career advisers or basketball coaches, and reaching out to offer help is part of everyone’s job.