Educate yourself about the topic
First of all, you should know what you are actually talking about. You cannot expect your subordinates to open up to you about their own mental health if they can tell you know nothing about such issues. So a good initial step is to take a training course, perhaps with a psychologist or coach, to learn properly about the topic.
Enable workers to balance their personal and professional lives
Work-life balance, stress reduction or burnout prevention: all of this must not just be theory on paper, but practice in your team. As Management Issues points out, there is no point in trying to talk to subordinates about the topic of mental hygiene and mental health without giving them the flexibility to put this knowledge into practice.
If you see signs of toxic behaviour or unhealthy work routines, call them out
If you observe someone, for example, behaving in a toxic way or being prone to workaholism, openly discuss the issue with your team. Use this practical example to explain what the problem actually is. Try to show subordinates how to apply what they have learnt about mental hygiene and sustainable working practices to their daily work.
Explicitly encourage subordinates to discuss their mental health with you
Last but not least, you need to create a healthy environment in which your rank-and-file workers are not afraid to talk about mental health. Repeatedly encourage your subordinates not to be afraid to come to you and, if they do, always listen to them and never take their concerns or comments lightly.
-mm-