If you (or your child) went to an expensive college, how did you pay for it?

My oldest has been accepted to several great (but expensive!) schools. Even after accounting for scholarships, there is still an enormous amount of tuition, room and board left to pay for. These schools have specific, 4 year programs (like a school within a school kind of thing) for her major (International Relations), so going someplace cheaper for 2 years may prevent her from transferring in to the program later. She does not qualify for grants through FAFSA. How on earth does one do it?