For off-campus access to library online resources, remember to follow the links from CLIO or this research guide. You can also use the proxy bookmarklet.
Can't find an article through our libraries' collections? Use Interlibrary Loan (ILL) to request a copy for free.
Google Scholar provides a simple way to broadly search for scholarly literature. From one place, you can search across many disciplines and sources: peer-reviewed papers, theses, books, abstracts and articles, from academic publishers, professional societies, preprint repositories, universities and other scholarly organizations. It is also very useful for seeing if other scholars have cited a book, article, etc. Search on the title, and then follow the "Cited by ..." link.
CLIO is the library catalog for the Columbia Library System (including Barnard Library, but excluding Teachers College and some information from the Law Library). In CLIO you can find books and media materials, search for different kinds of databases, and find articles within those databases as well.