Check that the Visual Editor is turned on by ensuring "Temporarily disable the visual editor..." is unchecked in your preferences on your main language Wikipedia (here on the English Wikipedia). (Visual Editor allows you to use a feature called "Citoid" which uses an API to get preformatted reference information (see the documentation for more details).)
The citation popup in visual editor, that allows you to automatically generate or manually create citations.
Identify a source that will help verify information on a Wikipedia article
Click after the sentence you want to add a citation to support
Click on the "Cite" button (looks like )
Autogenerate a citation using a URL, ISBN or DOI (this scrapes data from the page to create citations), or choose the second tab and fill in the appropriate citation fields for your source
The reference toolbar in the Wikitext editing interface, showing where to find the different types of citation styles.
Identify a source that will help verify information in a Wikipedia article
Search for the information you want to verify with a source, and click after the sentence
Click on the "Cite" dropdown menu
Choose a reference type (see the dropdown in the image on the right)
Fill in the relevant source citation fields
Wikipedia articles don't use any one standard reference style; though they favor the templates created by the tools described above, you can always write a plain-text citation.
Reliable sources for Wikipedia include any source with a history of editorial control (newspapers, books, finding aids, scholarly journal articles, editorially controlled websites). The stronger the reputation or the greater the authority of the author on a topic, the more well received it will be.
Though Wikipedia favors sources that are Open Access, it doesn't require them (after all, some knowledge can only be found in print books or behind paywalls). However, a reference to an open access source means that more public readers get a chance to find and read the research they need through Wikipedia. Make sure if you do cite a closed source, you use an unproxied permalink rather than a link specific to your institution.