Again, read the disclaimer from my last post. I'm not trying to write definitively, just illustrate a perspective.
1) Find out all you can about depression. Learn about the various types and how to recognize them. Realize that most depressed people hide it very skillfully, only letting hints peek out occasionally. (Often through self-depreciating humor.) Try to be aware and sensitive to those hints. If you are living the commandments, the Spirit will help you here.
2) Stay calm and rational if you begin to suspect someone is depressed. Otherwise, it will only show them you can't be trusted. This includes suppressing wild suggestions of obtaining therapy or medicine. Suggesting therapy is a great idea once the person is ready for it. Chances are if a person is depressed, they've already thought about therapy and rejected it for some reason. Listen first, make suggestions later. Sometimes a person just needs a listening ear before they will be ready to take action.
3) Tell them good things about themselves every chance you get. This doesn't mean fawning all over them, that's pretty transparent. But any time there is a real, positive attribute, emphasize it. Often depression fills your thoughts with worthlessness and self-criticism. It helps to have another external voice telling you that you're not so bad. Minimize the negative. Depression will fixate on any hint of criticism and expand it way out of proportion. Reinforce any negative that must be communicated with a dozen positives.
4) Make yourself slightly annoying. Push yourself into their lives (just a little). Depressives often shut out friendships, wanting to distance other people from their problems. If you can demonstrate friendship through the bad, you will seem like a real friend. Be ready for possibly harsh rejection at first. Realize that they are probably trying to protect you. If they harshly reject you, meet it with equanimity, an attitude of "No problem. Sorry I overstepped my bounds. I love you. You're a good friend. I am here for you as soon as you're ready."
5) Once they are ready, once they have verbalized their realization of a problem that needs fixing, suggest counseling. Offer to go with them as silent support. Counseling can be scary or embarrassing. It's a big step for someone to make.
6) Realize that you can't fix their problems, you can only be a support for them. Chances are, the boundaries of friendship will be pushed a little. It is a way for a depressive to test genuine friendship. If someone is violating the boundaries of friendship by coming over too often, taking over your life or refusing to leave when they ought, remember it is because they are afraid and you might be the only person they feel they can trust. Treat them gently. Rather than rejecting outright with a "go home", try to give them a "go home, but come back at [an appropriate time] tomorrow. I can't wait to see you again." Leave the door figuratively open after they leave.
7) Replace "I understand" with "I'm so sorry about that." No one - not even another depressive - really understands what it is like for another person suffering from depression. Even the depressive doesn't understand themselves fully. Show compassion, not understanding. It can be frustrating to feel that everyone around you understands you when you are lost in confusion.
8) Be ready to give support during some (often crazy) changes. Recovering from depression often means completely revamping your life. Thought patterns change, lifestyles change, even friendships change. Be there as a constant through the rough seas, and things will settle down again. Be encouraging through the changes and make sure you don't take them personally. Sometimes a person has to try out different things before finding what works.
9) Be honest. If a depressed person is becoming too much burden for you to carry and they don't seem to be doing anything about it, tell them. Tell them they have a problem you would like to help solve. Tell them you enjoy their friendship, but for this one thing that doesn't do them justice. Reinforce the limits on friendship with love. It might hurt them in the short term, but if you show
that "increase of love", they will realize you are a true friend through good and evil.
10) Get counsel for yourself. Go to your bishop or look for help online. Try to find a "friends of depression" type support group in your area. Being friends with someone so needy or so solitary may be hard, but it is worth it. Get help through the rough spots. You may need it.
At any rate, I hope these ideas help someone. I welcome any other ideas out there.