Losing a relative can be a traumatic experience, and you naturally want to help your friend through the process. The difficult thing is that every person processes grief differently. To comfort your friend after a relative's death, you have to listen to her needs, even when they go unspoken. There's no one right thing that you can say to make the pain go away, but you can be there for her in all the ways that you can.
Offer your condolences. Something simple like, "I'm so sorry for your loss" lets your friend know that you've heard the news and opens up the lines of communication.
Listen to your friend without judgment. She may go through a wide range of emotions, from sorrow to confusion to anger. She doesn't need you to debate her right now, or tell her that her feelings are wrong. She needs someone to be there for her.
Recall stories about her relative, if you know any. Celebrate the life of the person who died. Remember how her mom baked those great cookies when you came over after breaking up with your first boyfriend or how her dad used to take you fishing and would pretend to eat the worms.
Share experiences that you may have had with losing a relative. If you've also lost a mother or aunt, you could talk about how you felt and the things that made you feel better. You could talk about how you still miss the person or how you felt better after a certain amount of time. Note, though, that your experiences should equal your friend' — the death of a pet or a distant uncle is not the same as losing a parent or a beloved grandparent.
Bring over a few re-heatable meals. In the chaos after a death, your friend may not feel like cooking. Having something easy to cook, like a lasagna or soup with fresh bread, can ensure that she gets the nourishment she needs.
Do something together that makes her feel better. This will be different for each individual. One friend may prefer sitting together and watching a funny movie, while another will want to go out to dinner and talk about the lost one.
Suggesting that the relative is "in a better place" may not make your friend feel better, especially if she's not strongly religious or doesn't believe in an afterlife. Even if she does believe that her relative is in heaven, that doesn't always make the loss of the relative to those on Earth any easier.
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