Accelerated BSN (bachelor of science in nursing) programs exist for people who already possess degrees in non-nursing majors or concentrations. You would have to complete all of the prerequisite courses. Then the actual accelerated BSN program is anywhere from 12 to 18 months.
Many people with non-nursing degrees also opt to complete either LPN programs or RN/ADN (associate degree in nursing) programs at community colleges, trade schools, or technical colleges. People choose these options due to cost, financial aid issues, previously low grade point average, and a whole slew of other reasons.