Do NOT be silent. As soon as you become aware of the pain in someone's life, take action. This can be as small an effort as you decide, but DO take action because it will show the affected person that they are not alone and are cared about by others.
Encourage. Even if you haven't gone through the same thing as the person who is suffering, you can encourage them by offering cheer and hope. Smile. It offers light in a dark time. Laugh, share humor. Do not feel obligated to remain remorse and sober in fear of offending the sad person. What they need is to be brought up, not kept down.
Support. Often, sad folks become depressed and forget to take care of themselves. You can send them uplifting items anonymously, which I believe is best. This way, if you do more than one thing it can be interpreted as being cared about by many. Send an inspirational card, leave or send a flower, leave food baskets, or give a gift card to the grocery store or someplace fun like the movies. Reaching out can make all the difference in a person's life, helping them to cope with sad circumstances.