Once you've selected your topic, you'll need to identify find potential source works for your research.
The internet has really (really!) simplified at least one portion of this stage in the research writing process: you can now use the internet to search most libraries and online databases by subject keywords - and save the results in your personal datafile. If you like, of course, you can also dig through the card catalog and the printed reference indexes in the library - but for most research projects, searching reference databases available on the internet will render pretty thorough results.
Some of the more general services for this "background research phase" include the Library of Congress, PsychInfo, Lexis, the Humanities Index, PubMed, or the MLA International Bibliography, Ingenta, and amazon.com. Some of these services are available for free (see the listing below of the services you can search online for free), but a fair number are only available only through library systems or your organization's network.
Check with your librarian to find out which databases are available to you, and which are best for the type of research paper you are working on.
A word of advice about the internet: it undeniable that the internet is one of the most valuable research tools we've seen in quite some time. Nor is it any secret that there is a lot of information, on just about any topic you can think of to type into a search engine, available on the internet. Much of the information you will find through direct searching (using, for instance, Google or a similar search engine), however, is inappropriate source material for a research paper. If you have located a site or source you think might be useful, make sure you check with your instructor or librarian before relying too heavily on it as a source work.
The Library of Congress is another good place to start researching a topic, though here you will find only books. Every book published in the US is listed, though, so you'll have a lot of material to help with your search for a topic.National Libary of Medicine, PubMed site
The National Library of Medicine indexes article published on medical and biomedical subjects. Searching the publications database is free to the public.American Psychological Association, PsycArticles
If you are working in Psychology, you'll want to search the APA's PsycArticles database. Full text delivery of articles is available for a fee.American Psychological Association, PsycArticles
If you are working in Psychology, you'll want to search the APA's PsycArticles database. Full text delivery of articles is available for a fee.LexisOne
If you are working in a legal studies, LexisOne offers free searching of case law. Full texts of cases and other materials are available for a fee.