Define the scope of your research so you can narrow your search. You have to be able to explain what kind of research you are doing in order to find the grants you would be eligible for. Most research grants outline specific academic requirements the recipient must meet in order to apply for the grant.
Check the library first. The reference section of most university libraries has a small section of directories which list research grants available to students. The librarian can assist you in locating these directories. Most grants are categorized by college or department, for example, if you are studying literature you would look for grants in the arts directory.
Check the internet next. If you can not find what you are looking for in one of the library directories try going online. Some government grant directories are available for sale online at the GPO, US Government Printing Office. These directories may be available for free in the library but are not always the most up-to-date.
Ask your professors. They may be aware of research grants that are not widely publicized. Many private organizations or benefactors that provide grants only rely on word of mouth to find potential applicants.
Write inquiry letters to organizations which are prominent in your field of study. They may also provide research grants but do not advertise.