The primary difference between these disciplines is what is studied. In anthropology, the societies of people, past and present, are studied, while in psychology, the emotions, thought processes, and behaviors of individuals are examined. Both disciplines have many branches, and there can be some overlap between them.
In anthropology, the culture of an indigenous people might be studied, or the culture of a contemporary urban environment. There is a focus on customs and artifacts, which help the anthropologist understand the society better. An anthropologist might study a culture of hunters and gatherers, to gain some understanding of our evolutionary roots, which might give some insight into how we feed ourselves today. An anthropologist might study what is found in a burial mound, to understand the religious beliefs of an ancient society. Anthropologists may also study language, to see how language influences particular societies. It would be interesting to see what an anthropologist makes of Facebook!
Psychology is just as wide-ranging a discipline, with many branches and schools of thought. Psychology can involve studying those who are mentally ill or those who are well-adjusted. Psychologists study human behavior and also, finally, have some interest in the human brain and neurology, which we have come to understand, is the basis of human emotion and behavior. Some psychologists are educational psychologists who want to know how people learn. Others are organizational psychologists who study how people behave in groups, such as in the workplace. Psychologists can bring to bear their knowledge for sports teams, to help a team perform better as a team. I am not sure I would want to know what psychologists make of Facebook.
Since it is hard to study a society with a complete disregard for individuals in the society, and since it is impossible to study human behavior without examining that behavior within the context of a particular society, there is some inevitable overlap, and even when there is not, anthropologists and psychologists can provide valuable insights and make important contributions to one another's disciplines.