Plugins are available that will automatically check for free copies of articles you've found online.
Unpaywall looks for articles that are open access or uploaded by the paper's authors. Whenever you come across a paper whose full text is freely available, a green open padlock will open on the side of the web page.
All plugins are available for Google Chrome and for some versions of Firefox. They can be installed from the Chrome Web store and the Add-ons for Firefox page.