Whenever it comes to depressed or anxious people, it can become really hard to deal with.
First, and a lot of people forget this, is that it's not on you to solve their problems. One person trying to take on all the problems of another often person drags both down until both are anxious and depressed. That being said, there are still some things you can do to help them.
The best people to deal with the problem are also unfortunately authority figures that have all sorts of limitations. Psychiatrists are best, followed by maybe school counsellors, teachers (who have to report it, and can move it along the right channels), parents, etc.
If you can't do that, or if you want to help on top of that, there are still good friend things you can do. That's your roll in this - good friend. Invite them out more, specifically to do things that build your social life. Camping is particularly great - you get bits of natural exercise, sunshine, bright colors, cool breezes, etc. Going to the park is great for the same reasons. Joining a club with them is wonderful. Some people choose religious ones (I don't, they're too preachy and stupid for me), but others simply do things like chess club, sports, really anything that's social after school.
You could also teach them some good techniques for stress management. Meditation, listening to music, taking a deep breath, writing, etc. That's if they're looking for ways to relax of course.