How did people cope with the problems they faced during the Depression?
First of all, you should realize that there may be a specific answer in your text that you are supposed to give. This is a very broad question and different texts may well answer it in different ways.
The general problem many (but by no means all) people had during the Depression was poverty. There were few jobs and so many were poor. There were various ways of trying to cope.
For example, many people tried moving to find work. The Okies were a major example of this as were hoboes. Other people turned to whatever family members might be well-off enough to have a job. Family history in my family says that my great aunt who was a teacher in Cincinnati sent money back to Idaho to help her parents who had a farm.
You can also talk about how people tried to cope through entertainment. Movies were very popular in the Depression and they tended to be extravaganzas that were meant to wow the people and make them forget their problems.
Again, there are many ways to answer this...