As an applicant for a student visa to the United States (F-1 or M-1), you are expected to prove that you can cover the cost of your school or college tuition and living expenses. This means that you'll need to cover not only your own costs, but those of your spouse and children, if any will be staying on with you in the United States. What's more, you'll have to do this without relying on any employment that you might pick up in the United States while studying there—and without your spouse or children working at all. (See the U.S. government's Foreign Affairs Manual at 9 FAM 402.5-5(C).)
We'll explain what that means for the visa application process here. The bottom line is that if you can't show sufficient funds in advance, you won't be granted a student visa at all.
If you will be applying for an F-1 (academic student) visa or status, your financial resources must clearly cover a 12-month academic term. And, you will need to show indications that your additional years of study will be covered, as well. The U.S. government doesn't expect you to literally be able to pay for all your years of education right away, but it does expect you to show where the money will eventually come from.
Similarly, if you will be on M-1 (vocational student) status, your resources must cover your entire 12-month (or shorter) study term in the United States.
Your sources of financial support can include personal funds; personal assets or property that are readily convertible to cash; pay from work that you do as part of a fellowship or scholarship; or specified funds from other persons or organizations.
As part of the visa application process, you will need to gather documents that will supply proof of the existence of these things. For example, you might show evidence of:
If your family members will be supporting you, they can use a USCIS Form I-134 to indicate that they not only have the income and assets you've shown, but they are willing to spend them on your studies and living expenses.
If individuals who are not members of your family are willing to support you, use any of the types of evidence mentioned above with regard to family members, including a Form I-134 Affidavit of Support.
The U.S. government official who decides whether to issue your visa will wonder, however, why someone who is not related to you will want to pay for you to get an expensive U.S. education. For that reason, non-family members should also write a sworn statement explaining why they are so willing, able, and motivated. The statement should mention that the person understands that they are not just a "backup" if other sources fail, but will be immediately responsible for paying all or part of your tuition, fees, and expenses. And of course, if there's some personal connection that wouldn't otherwise be obvious, like that person being your best friend's parent, that would also be good to mention.