Your friend would appreciate having you around. Many people with depression find it hard to maintain their relationships with others. Given their persistent low mood, they tend to be pessimistic in their outlook and like to harp on events that went wrong in their lives.
If they keep talking all about the negative stuff in their lives, their friends usually will not enjoy their company very much. So the most important thing that you can do is to keep your friend company, allow him or her to talk and ventilate and validate his or her feelings.
When listening to your depressed friends, it will good to hear them out first and not interrupt them too early or too frequently. It is important to exercise some self-restraint and not to offer quick advice or suggestions as they will feel that you doubt their level of intelligence. If their problem can be easily solved, they would have thought of the solutions themselves.
The other tip that I can offer is that: whether the depressed individual decides to take medications or to undergo therapy, it will take many weeks or even months before the mood may improve significantly. So it will be important if you can encourage the person to persevere with the treatment and not to give up too easily. If they have side effects from the antidepressants, they can discuss with the doctor to see if the dosage can be lowered or the person can be switched to another antidepressant.
An important psychological intervention is behavioural activation. This means that the person needs to schedule activities for himself or herself. You can keep your friend company by going for long walks together, cycling or catching a movie. If the depressed person were to keep staying at home and not participate in any activities outside of the house, there is a high chance that he or she will just keep thinking of negative things and wallow in self-pity.
Thank you for being around when your friend needs you the most. Do work closely with the mental health professional so that your depressed friend will be out of the woods soon.