The other answer is mostly correct except for the fact that student loans *are* most certainly a part of financial aid. Financial aid includes loans, grants, work study, and one could even throw scholarships in there as well. When you fill out the FAFSA at www.fafsa.ed.gov you are applying for federal and state financial aid which includes grants for very poor students, and loans for all students, plus work study for those who are interested and qualify.
To go to an expensive school, you will most likely need to take out private loans which are credit based and require a cosigner. Since it goes on their credit, you need to be very careful with whom you ask to cosign.
When it comes to paying off student loans, you enter repayment 6 months after you graduate or fall below half time attendance. You cannot get out of student loans by filing bankruptcy or waiting on them to fall off your credit. They never, ever go away until paid. Defaulting on a student loan is the worst thing you can do. Taking out loans is easy to do, but many students freak out when it comes time to repay. If you can't afford a school without taking out more in loans than you'll make in your first year after graduation, pick a cheaper school.
Obviously if you want to go to an ivy league school you better be the best of the best academically. If you are actually ivy league material, you should be able to use your intelligence to google appropriate resources to learn more about financial aid and college in general. Good luck.