Check the deadlines for your particular state (See Resources.). Apply using the online application at the Federal Student Aid site. Have all your personal and financial information at hand as you fill out the form. Make sure you list the school code of the college you want to attend on the application. Otherwise the school can't receive a copy of your paperwork.
Consider asking for federally backed student loans if you qualify, since many of the needs-based grants may already be exhausted by the time you apply (or at least the school may not have available as many grants). For this reason, you will want to apply as quickly as possible. But keep in mind that unlike the grants, the loans have to be repaid.
As soon as your application is completed, go to your school's financial-aid office and ask for them to download you information from the FAFSA site. Having them do this immediately (rather than waiting for the government to get around to sending it to them) will speed up the process.