It isn't hard to find peer-reviewed sources: you just need to know where to look! If you start in the right place, you can usually find a relevant, peer-reviewed source for your research in as few clicks as a Google search, and you can even use many of the search techniques you use in Google and Wikipedia.
The easiest way to find a peer-reviewed article is by using one of the Library's numerous databases. All of the Library's databases are listed in the Online Journals and Databases index. The databases are divided by name and discipline.
Departmental libraries and library subject guides have created subject-focused lists of electronic and print research resources that are useful for their disciplines. You can search the library directory for links to the departmental libraries at the University of Illinois Library, or search library websites by college if you're not sure which departmental library serves your subject.
There are numerous print and digital resources for specific disciplines, areas of study, and specialist fields. To find research resources and databases for your area, consult the comprehensive directory of LibGuides, the websites of specialist libraries, and above all, contact a librarian for help!
Here are a few major databases for finding peer-reviewed research sources in the humanities, social sciences, and sciences: