Oh I'm so glad you've asked! I was a depressed child and the way my parents handled it was, well, awful, but there was other stuff going on.
I think it really helps if you step out of it mentally (as in, stop thinking of it as helping *your* child) and think of it as how would you help teach a friend how to cope with depression. If she truly feels depressed, it probably will not be the only time in her life, and being able to identify the signs and symptoms will be very helpful to her.
Don't pry into why she is upset, just sit down with her and try to analyze her feelings with her. Perhaps google a list of signs and symptoms beforehand so you have some talking points if you've seen some in her. Then talk to her about how its okay that she doesn't feel comfortable talking to you, but that she needs to find someone she does need to find someone she is comfortable talking with - perhaps a guidance counselor, a teacher, coach, and offer therapy outside of school if she doesn't feel like talking to anyone there.
When all the heavy stuff is out of the way, then talk to her about little things that make her feel better when she does them - maybe its something as small as taking a bubble bath or going to the movies. Maybe even help her make a list and remind her that she needs to do things for herself - especially when she's feeling down. Let her know that she can come to you at any time and say "Mom, I'm having a bad day" and ask for something off the list if she cannot take care of it herself.
My parents expected me to tell them everything and if I didn't, we had a lot of problems. It wasn't always stuff that I was trying to keep secret from them, sometimes I just didn't want to talk to them for whatever reason. I really wish my parents had taken my bouts with depression more seriously and explained them to me - that extended sadness isn't okay and guided me into how to deal with it. Sort of just treat it as one of those "must do" parenting talks without going into detail as to why she's currently feeling that way - she'll probably still be a bit standoff-ish about it, but treat her like an adult and work out a plan together and she'll appreciate it for life.
I just wanted to add that my parents pretty much just shoved me into counseling when I didn't talk to them and while it helped having a counselor, it didn't help that it was pretty much just taken care of for me without explanation. At her age, she's old enough to be part of the process and needs to understand why xyz are being done. Most depressed people do not realize they are depressed themselves - especially not the first time around.