Contact the department of student financial aid services in your school. Most colleges and universities have a standard protocol for appealing for financial aid. You may only have to fill out a form detailing your economic situation, or you may have to write a letter, or do both. If you do have to write an appeal, find out who to address it to.
Type your letter instead of hand writing it. Begin by thanking the college for accepting you and for any financial aid it has already offered. Be courteous and gracious, but make it clear that you require more assistance. You should tell them that you will not be able to attend school without the aid you are requesting.
Explain why you will not be able to pay. Use information about your own financial state of affairs and your parents' finances to show how you are unable to afford college. If your parents would be unable to afford the loans they would need to pay your tuition, for example, explain that in your appeal.
Detail any extenuating circumstances. For example, if your parents are already in quite a bit of debt, they may make enough money to disqualify you for financial aid and still not be able to pay. If the college knows this, they may be willing to make a special exception and grant you financial aid.
Reiterate that you will not be able to attend school if you do not receive financial aid. Take a courteous but direct tone. Make sure to end on this note, since it is the main point of your letter.
Double check your mechanics. Make sure that your letter is well-written and has no spelling or punctuation mistakes. Use formal language to sound professional.