What TheNewGirl says is spot on!!
As someone who suffered/suffers from bouts of depression/anxiety and as someone who is included in a variety of support networks for different people, I find myself familiar with this topic. Depression in all its forms nowadays seems to be something to be ashamed of. It's definitely true that most people may not want to talk about it and a large portion of that desire comes from the labelling/diagnosis process. Nobody wants to be told they have a mental health issue because the connotation of that statement boils down to = crazy/psycho. Personally I'm only starting to see more active campaigns towards the struggle against these sort of issues. My mom has clinical depression so it's something that I have to experience everyday. I have friends who are going through tough times right now (mostly in their early-late 20's).
You have to take in account that while you're sitting talking to one another, your energies are connecting. Depression/negative energy is contagious and first and foremost, always protect your own energy/mind set. Remind yourself that you're there to help this person and if you start feeling under the weather, you need to know when to take a step back and recharge. If you drain yourself too quickly, you won't be able to successfully assist them. I'm very sensitive to energies/vibes so I really have to know my limits or else I'll start spiraling downward too. Maintain a positive attitude/mind set always. Use your positive energy and thoughts to heal the space you're in or as someone once told me "be the light unto the darkness". You don't have to speak to do this. You love this person so let your love emanate in your body language and reinforce your feelings with your eyes. Maintain eye contact and express warmth/compassion in your actions. 93% of human communication is NONVERBAL. Sometimes you can support someone without saying a word or even when you aren't with them but are thinking about them, you can send out positive vibes/energy and good intentions/love for them into the Universe.
I choose to be empathic over sympathetic and compassionate over judgmental. Always give them a safe place to come to and your relationship with strengthen considerably.