Piaget's theory of constructivism states that learning is ultimately in the hands of the student, not the teacher. His theory stresses that people, especially children, cannot just be given knowledge, rather it must be individually constructed from personal experience. Part of this theory is Piaget's conception of "ages and stages," outlining what children are capable of understanding at various ages and how they form and modify perceptions of the world as their knowledge and cognitive abilities continue to grow.
Assimilation and accommodation are two complimentary processes of learning Piaget identified that serve as key tenants of constructivism. Assimilation is when newly learned information is simplified to fit into preconceived categories and notions of how the world works, when you take a new idea and make it fit your previous knowledge. Accommodation is when you must shift your view of how the world works and invent new mental categories in light of new information.
Just because Piaget's theory maintains that knowledge must be personally experienced does not mean he believed teachers to be unimportant. On the contrary, he saw teachers as very important, just in different roles. Constructivism reframes teachers as facilitators, working with the student to help her build her own understanding. Rather than lecturing answers, constructivist facilitators ask them questions; rather than telling students facts, constructivist facilitators engage them in conversation, helping them to reach their own conclusions.
Having students work in groups or pairs and present their findings to the class is a classic example of constructivism in practice. Working together allows students to discuss and explore the material on their own and encourages them ask each other questions and attempt to find answers on their own. Constructivist classrooms also favor primary sources over textbooks -- reading the Constitution itself instead of reading someone's opinion on it, for example, makes it more meaningful for students and better enables them to explore it at their own pace and understand it at their own level.