The most obvious conflict is that of racism and prejudice. The Youngers are a black family moving into a white neighborhood. The neighbors try to pay them to move away and then resort to threats.
There is also conflict with Beneatha wanting to be a doctor and the cost of her school. She believes she deserves the money more than anyone else for her education.
Other family members have ideas about how to spend the money as well, so there is the conflict of the money and how to spend it.
Walter takes the money for a "get rich quick" scheme and gets conned out of it. He takes away the conflict of how to spend the money and replaces it with how will they afford the new house in addition to their resentment of him and his stupidity.
Beneatha also suffers from the internal conflict of whether or not marry her African boyfriend and move away from her family and all that is familiar and safe.
Lorraine Hansberry's A Raisin in the Sun is a drama that contains the conflicts of Person vs. Self, Person vs. Person, and Person vs. Society.
Person vs. Self
Beneatha struggles with her identity as she tries various hobbies. She wants to be able to express herself honestly, and she wishes to become a doctor and be independent. She wrestles with trying to assimilate into a white world as she straightens her hair. She feels some pressure to marry into money, but she does not love George Murchison, and she is conflicted about marrying Asagi and going to Africa with him.
Walter is dissatisfied with his job as a chauffeur. He would like to be more self-directed and to be able to provide for his family. But he is also selfish because he wants to get rich quickly by investing a large part of his father's insurance money in a liquor store.
When his so-called friend runs off with his money, Walter feels terrible, but he decides that he must be the man of the family.
Ruth is very disappointed in life: "Life has been little that she expected." She wrestles with whether or not she should have an abortion, because she and Walter cannot support themselves and their son Travis now.
Lena (Mama) is the matriarch of the family and is a strong woman who struggles to maintain her belief in traditional values, which go against many of the things her children do and say. But she reminds herself of how her husband always lived for his children and how, when he was exhausted and mentally worn out, he replenished his soul at home through his joy in his children.
Person vs. Person
Walter/ Beneatha: Walter comes into conflict with all the other characters. In fact, his words to others are said to always be like an "indictment." As he and Beneatha argue, he tells her,
WALTER: I don't want nothing but for you to stop acting holy 'round here. Me and Ruth done made some sacrifices for you. Why can't you do something for the family?
Walter/Ruth: Their marriage has problems, and they are financially strapped, having to live with Mrs. Younger. Walter complains that Ruth "couldn't be on my side" many times. Poor Ruth just replies, "Walter, please leave me alone" when he seeks her support for his idea of buying a liquor store with another man, because she is pragmatic and he is more of a dreamer.
Mama/Beneatha: As an educated person, Beneatha perceives herself as a modern woman, and, as such, she rejects some of her mother's cultural values. Mrs. Younger becomes particularly upset when Beneatha displays her lack of faith in God and her hostility toward her brother. Beneatha's irresponsible expenditure of the family's money on new hobbies puts an unnecessary burden on the entire Younger family.
Mama/Walter: Walter greatly disappoints his mother when he loses thousands of dollars on his business venture when his so-called friend absconds with the money Lena gave him. Her faith is further tested when Walter argues that the family should take the bribe from Mr. Lindner, but when the man comes to their house, Walter speaks for the family and refuses the money.
Person vs. Society
The Younger family refuses to be intimidated by Mr. Lindner, and they move to a white neighborhood.