How can I support a loved one going through anxiety and depression?

This is a great question. As a person who has suffered from depression and anxiety in the past, I have a handful of suggestion to provide. I would suggest not to force the person into any of these things. Give them these suggestions and let them decide for themselves. Let them know you are there to help them for anything they need.
1. Meditate daily: When you start meditation, it seems useless. But overtime, you start feeling the benefits. For some people it takes days, for some months. But just learn to sit in peace with yourself.
2. Find a therapist you feel comfortable with: I went through 3-4 therapists and therapy styles till I found the right one. And I wouldn't want it any other way. I used to think therapy is useless, but now I swear by it.
3. Set time aside in the day to stress: For example, I used to set aside 8 PM to stress. When I would feel anxious about something I could not control, I would just tell myself that I will think about it at 8 PM. It takes practice but it helps.
4. Go outdoors or find a hobby group: As much as I love my bed and TV, just getting myself out there between people helped me so much. I would recommend it for everyone. Being in introvert, I used to hate being around new people. Now I just put myself out there and I know people almost everywhere I go for my hobbies.
5. It's ok to take medication. If anxiety and depression are spoiling your quality of life, it's ok to speak to a psychiatrist and see if they can recommend any medication. It almost was taboo growing up for me, but now I see the benefits.
6. Talk your partners / close friends and express your feelings. Take support from people around you. If they know you are struggling, they will be sensitive enough to help you out.
Hope this helps.