It is necessary for students to have a budget plan. The choice of your college and major would depend on a large extent on your ability to pay.
Students who are exceptionally bright or at the top of the class maybe awarded merit-based scholarship. The amount may vary from a few thousand dollars to a full tuition waiver!
There are many universities in the US that provide financial aid and international student scholarships to international students, both at the Undergraduate and Graduate level. However, this aid is usually limited and is often more readily available to Graduate than Undergraduate students. You must submit a financial aid application if you intend to seek financial assistance for your studies abroad. The policies regarding financial aid vary considerably.
Even if no assistantship is available at the time of admission, most Indian students manage to get some kind of financial aid from the university after one or two semesters. So it makes sense to go to the US for education if you can manage one year's expenses on your own.