Dealing with Loss as a Nonbeliever

I've never really been good at dealing with loss. It's bad enough when it's my own loss, but I never know how to handle helping people I know through their own loss. Basically every coping mechanism I had for dealing with death is based on my theistic upbringing.

Now, as a nonbeliever, I'm left without those options. I could say "they're in a better place," but it would be an empty sentiment since I don't really believe that. I could say "their pain is over now," but again, if they don't exist anymore, I don't think that's really much consolation.

This all comes up now because a friend of mine recently lost her husband of many, many years, who I'd never actually met. When I lose someone myself, I know that I can take solace in the memories I have of them. I can remember the time we spent together, the laughter and tears we shared, the good times and the bad. But when it's someone I only have a vicarious relationship with, I can't really relate to anything but the raw emotion of loss, and I don't handle that very well. I react awkwardly and tend to feel uncomfortable.

How do we deal with loss, ours and that of others?