How does one file for citizenship?

Generally, one must be a Lawful Permanent Resident (have a "Green Card") for five years before becoming eligible to apply for citizenship. Based upon details you mentioned, I presume that you do not have a "Green Card," and you are interested in your U.S. citizen older brother sponsoring you to Adjust Status to become a Lawful Permanent Resident. Unfortunately, there is a very extensive backlog for visas in the Family-Based Fourth Preference category - the category by which a U.S. citizen may apply for a sibling. While the backlog may appear to be shorter, in fact it may take 15 - 20 years (or even longer), and therefore this rarely is a satisfactory strategy for attaining Permanent Resident status. It may be worthwhile to explore other potential avenues to achieve your goals, such as an employment-based application related to the academic degree you plan to attain. There really is no substitute for conferring with an immigration attorney who, after learning all of the relevant details, would be able to advise you about immigration-related eligibilities, options and strategies. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.