Show true empathy:
Try to gauge the reason for their state and feel their pain. When they realize that you understand they will open up and that is the best cure. Show genuine concern. Be there to console when they break down and let them know that they call you any time. Tell them 'this too shall pass' which is the most comforting fact about life.
Convince to take outside help:
If you find some extreme forms of depression in them, then do call for medical help like counseling, anti-depressants and electro-convulsive therapy. Some people might not agree to be treated and you are needed here. You need to convince them that it is better for their health and that there is nothing embarrassing about it. If they have already availed medical help, take care of their medicine routine and regular check ups. Do not let them leave the process incomplete. Take care of their food intake as most depressed people either under eat or over eat during that period.
Indulge in activities:
Being a family member you will know the activities they like. Some get lost in reading and forget everything while others believe a good movie rubs everything away. Encourage them to indulge in such activities and do it with them together to make it more fun. Walks, long drives and sports also act as comforting outlets and the exhaustion can lead to a good night sleep which is the best anti-depressant.
Do not give up and keep your nerves:
The most important thing is to keep your own nerves and do not break down yourself. You have to be patient and strong enough to deal with the mood swings and rejections. Consider it just a passing period of life which shall pass and happier times will come. Do not be disheartened if a depressed person misbehaves or makes acidic comments because you know his state of mind.