This page in a nutshell: About finding sources to support a specific Wikipedia article. For finding a source you have already identified, see Wikipedia:Find your source.
Independent and reliable sources are vital for creating encyclopedia articles. Reliable sources allow editors to verify that claims in an article are accurate. The higher the quality of the source for the statement it backs up, the more likely that statement is to be accurate. Independent sources help editors to write neutrally and to prove that the subject has received note. Wherever possible, editors should aim to use sources that are independent and highly reliable for the subjects they write about.
Many of the best sources are not available online, or are only available under subscription. For example, many books are not available online at all, and subscription to academic databases such as JSTOR can be fairly expensive. However, it is possible to use the open web to find many good sources to use in writing encyclopedia articles. Examples of such sources are news stories from newspapers with a reputation for accuracy, books which have previews on digital libraries, and academic papers which are available open access in open archives.
Theses and dissertations: works created as a requirement for the completion of an advanced postsecondary degree. This page describes some of the considerations in using these types of sources.
Websites, blogs and other user-generated sources: online content from a variety of authors/publishers. Reliability depends on the editorial control of the website. This page discusses issues with user-generated content.
DuckDuckGo or other general search engines are effective for finding online sources in particular, but can also be used for some other kinds of sources depending on the topic area. This video outlines the fundamentals of "advanced search" techniques.
User:Syced/Wikipedia Reference Search provides a Google Custom Search that can be used to efficiently find sources on certain websites that some Wikipedia editors have determined are generally reliable, overall. Some hits (such as opinion pages) may not necessarily comply with WP:RS, so judgment is still needed. Because this search only includes returns from a pre-determined list of candidates it could miss many others possible sources. Nonetheless, this tool can sometimes be a good starting point.
To help find sources, Wikipedians have developed a number of source-finding templates which link to searches most likely to find references suitable for use in articles. The most well-known of these is ((find sources)), an inline template which can be used almost anywhere. (But please don't use it in articles themselves.) This template allows editors to tweak search strings to find the best match for the subject; see the documentation for details. Alternatively, users who desire more freedom can use the meta-template ((find sources multi)), which allows a choice of search engines.