If you have a US passport and are applying to a US college, you do not need to submit a financial statement even if you mistakenly receive a form asking you for one. If, however, you are not a US citizen, you will be required to obtain a visa from the US Department of Immigration before you travel to the US to attend college. 

To be eligible for a visa, you must demonstrate that you have sufficient funds available to pay for your expenses while you are in the US. Therefore, you will have to submit a "financial statement" listing the names of the persons (probably your parents) who will be paying for your education. You may either use the university's form or this generic financial certification form from The College Board. Most colleges require the form at the time you apply, but a few don't ask for this until you've been accepted.

As part of this documentation, you will have to provide a statement from a bank certifying that funds are available. Since many bank officials are naturally leery of signing a form they don't completely understand, they may not want to certify the form. In that case, ask for sufficient official copies (one for each college where you'll be applying) of a financial statement of account or a letter written in English indicating your parents have sufficient funds available to support your college expenses, and attach it to the form provided by the college. That approach is perfectly acceptable to almost all colleges.

Once you've been accepted and decided to attend a particular school you will take your I-20 form to the American Embassy in Singapore to get your F-1 visa. Please carefully review the information on the website for information on securing your visa.

If you are not a US citizen but are looking for financial aid to attend a US university, eduPASS provides excellent information. A list of colleges and universities that provide aid to international students is included.

US Immigration and Visa Sites

INS
The United States Immigration and Naturalization Service provides a range of information to introduce you to the INS.

The Bureau of Consular Affairs
Information about the issuing of visas to individuals hoping to study in the US. 

EducationUSA
The Bureau of Educational and Cultural Affairs at the U.S. Department of State provides this international student-focused website.