An exchange program is a reciprocal agreement between two or more universities that allows students to pay regular tuition on the home campus, but study at a foreign university. There are programs available for students at all levels, and with careful planning students can study abroad from the sophomore through senior years.
Graduate students can also participate in study abroad.
Start thinking about it your freshman year. However, a year in advance is usually sufficient. A semester in advance is okay if your plans are specific. Students can study everything from social sciences to the natural sciences, business to technology, liberal arts to performing arts. It's possible to go for either an academic year, a semester, a summer, or a vacation period, depending on the program you choose.