The typical sources of college financial aid include the federal government, state governments, the colleges themselves, and private scholarships, and they all play important roles. That being said, the largest distributor of financial aid is typically the federal government.
Federal aid comes in a variety of forms such as grants, work-study programs, and loans. Pell Grants, for example, are need-based grants that students don't have to pay back. However, the federal government also provides subsidized and unsubsidized loans that do have to be paid back.
On the other hand, colleges themselves also offer a significant amount of aid – especially private colleges with large endowments. This can include both merit-based and need-based scholarships, sometimes covering the majority (or even all) of a student's tuition. Some colleges are even "need-blind" and "meet 100% demonstrated need," like Vanderbilt, which essentially means that they do not take your financial situation into account during the admission process, and once admitted, they promise to cater for all your financial needs, respectively.
Private scholarships are another source of aid, but on the whole, they account for a smaller fraction of the aid received compared to the aforementioned sources. These scholarships can be highly competitive and come from a variety of sources, such as companies, nonprofits, or community organizations.
In conclusion, while all of these sources can contribute to covering college costs, the federal government and colleges themselves typically provide the most financial aid.