First and foremost, be patient. This is a wound that will only heal with time. And don’t worry. There’s nothing for you to fix.
Be supportive. This refers back to patience. You will temporarily have to pick up some extra responsibilities, because there are things your loved one can’t do right now, like dishes, running errands, or laundry. They just can’t. They’re not being lazy, they are actually incapacitated.
You will also have to help them with self-care, by reminding them to eat, shower, and brush their teeth. If they are not sleeping well, buy an over-the-counter sleep aid and remind them to take it, because if they sleep poorly, that will drastically worsen their depression. Inversely, if their sleep gets better, they will have an easier time with their depression.
Since this is what is considered a situational depression, these problems will not be long term. The depression will probably be over in less than a year, and will gradually get better day by day. It may even be better in a few months, depending on how quickly your loved one processes their loss.
If you can make an appointment for them with a therapist, do so, and offer to drive her/him to her/his first appointment. If they hate the therapist, try again with someone else. A therapist can teach your loved one coping tools that will help ease her/his 
suffering. You can learn coping tools alongside your loved one, both for you to use yourself, as well as for you to remember so that you can remind your beloved to use specific tools. If you would like to borrow some of my tools, I have a list here with explanations of how to use them: Coping Tools You Can Borrow! – The Goldfish Painter
Let them be angry, and remember that if they get angry with you for doing nothing wrong, it’s their grief talking and that their anger probably has nothing to do with anything you actually did or didn’t do. Try not to take it personally. This is normal for grief and will pass.
Let them cry. You don’t have to say magic words. You can’t fix this for them. “I’m so sorry that you hurt so much”, “I love you, and I’m here for you, just tell me what I can do to help” and “These feelings won’t last forever, please don’t give up” are all good things to say, and they might really help. You can help; you cannot cure.
Appreciate the good moments, and when one comes along, slow down and take it in. Getting even just a breath of relief can give you and your loved one the strength to carry on in this fight with depression.
If you act with love and stay patient, you will be doing what your loved one needs. Make sure you look after your own mental health so that you can continue to support their needs. Carve out some time for yourself and take it, so you can return to the situation refreshed and capable. You are the caregiver here, so the top priority is that you care for yourself, so that you can continue to help your loved one.
You should be proud that you’re reaching out in search of ways to help your loved one. That is very kind and compassionate. I wish you all the best, and I hope you see some beauty in the world today.
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