Do you need the article right away? Use the following tools to find out if a free version of the source you need is available online. Note that these may often be pre-prints and not the final version of an article as it was published in the journal.
EndNote Click (formerly Kopernio) is a browser plugin that finds the best available PDF of an academic article while you browse. Behind the scenes EndNote Click will search open databases and (where possible) your university's subscriptions to find the best version of the paper for you.
Search the full text of books and magazines that Google has scanned.
Find out which university the article's author is affiliated with, then check that university's library website to see they have an institutional repository. You can search the institutional repository to see if the author submitted their work to it.