He, I'm an international student and I am aware that I am not eligible for FAFSA (if I'm not wrong?). How do I apply for financial aid?
As an Int'l student you are not eligible for and US Federal or State grants so you are correct.
Nevertheless, many colleges do allow Int'l students to apply for financial aid.
What you need to do is review all the information regarding Int'l students on each of the websites of the colleges you are interested in applying to.
So if there are 10, you need to go to each college's website and review in detail all the information they provide. If the information is unclear or requires more explanation, then contact the financial aid office at the school in question. That is far more efficient and better use of your time than asking for specific answers about Int'l financial aid here.
In general, you have to apply to the schools first and then follow the process they instruct to apply for financial aid. I'm attaching a link to the CSS profile which is a form that many US colleges use to determine financial aid for Int'l Students. In addition to submitting the CSS profile to the colleges you want to apply for, they will be giving you a list of additional documents once you submit the CSS profile. For instance, the may wish your parents, both the custodial and non-custodial parents (if your parents are divorced) to submit their financial records like TAX FORMs, or other business records if they own a business or a farm. This is the same process all Americans have to do as well so you just have to follow along as well.
https://cssprofile.collegeboard.org/international-applicants
Keep in mind that very few schools have generous financial aid packages for Int'l students. There are many colleges but only a few that pay the majority of the costs. I'm submitting a link to those as well. These are very hard schools to get into, some accept as few as 4% of their applicants so they are not for everyone.
Good luck with your research and college admissions process.
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@nerdartsy I was planning on typing up an answer for you but @CameronBameron provided you with a great response. There really isn't anything else for me to add onto here! The process for applying for aid is complicated, even for American students, so try not to get too discouraged. And as @CameronBameron mentioned, receiving aid as an international student is very difficult. If you're not offered aid don't think it's because you don't deserve it, it's just not something that is done often here.