The above posts are correct - look in the library first. Libraries have tons of free info just begging to be examined.
That said, you can supplement your research by visiting http://www.carl.org. The Carl Corporation runs a nonprofit database (in the UnCover section) that includes articles published in peer-reviewed journals. This available research only goes so far, however. If your subject was Civil War, for example, you could go to UnCover and key in “Civil War” as your keyword and get some ideas as to which journals cover what you want. Then you can go to the libraries themselves and request those issues. You can read abstracts (or in some cases, just the titles) of the articles for free on UnCover, but to read the entire article you have to pay to download.
Also, if you go to http://www.publist.com, you can get lists of tons and tons of journals from which to choose. Once you know which journals fit your needs, you can either get them from your library or maybe even research a little online (some professors, I suppose, don’t like online citations). Some peer-reviewed journals DO have their archived journals available online for free; you just need to make sure you get the entire citation: “J Am. Med. Soc. 6(13), pp56-90.”