First and foremost, when your child comes to you expressing how they feel, please sit there and listen to them. It took them a lot of courage to put their thoughts together and actually approach you about this. They thought about it several times before actually coming to you. You can be besties with your child and share such a close bond, but trust me when I say it took them a long time to come to you. So seriously take the time to hear them out.
Second, mental health disorders exist. Depression, anxiety and everything else all exist. I understand that you might think that your child is just sad or stressed out for a specific short-term reason. But, in a world full of resources and access to technology and the internet, your child most probably did their research. They googled what is mental illness and the symptoms and everything else about it before coming to you. They most likely self-diagnosed themselves and need your support to take the next step. So do not shut them down when they come to you.
Third, please educate yourself. Just like how your child most likely did before approaching you. It is common that people in your generation do not know what exactly is a mental health disorder because you guys have not experienced them to the extent the younger generation has. For example, I often hear parents tell their child that you seem all happy and you talk a lot, so you aren't depressed. Just because someone has a smile on their face, that doesn't mean they are happy, I am positive that you hid your feelings before from people and faked it in front of people. So please don't assume things and educate yourself on the topic.
Fourth, one very important thing you need to understand is that you and your child grew up in different situations and circumstances, and thus your problems are different and cannot be compared. Often parents tell their children that they went through struggles too in their lives and made it fine without any cry for help. I understand that you had your own troubles and problems and in comparison, your problems may seem bigger and worse to you. But your problems were different, the situations that caused the problem are different, and the circumstances you were in are different. So no comparison is even possible. The society is different now. There are other external and internal factors that affect your child. Most of these factors were not present during your times. So seriously, stop belittling your child's problems or mental health disorders because you think you had it worse.
Lastly, just be there for your child. I can't emphasize that enough. No matter how many friends they have and other close people they have in their life, at the end of the day, they look at you as their biggest support. If they come to you with their feelings and problems, listen to them and consider their feelings. The worst thing you can do is make your child feel like they can't come to you and that is not only going to break them, but also create a major disconnect between you two.