Wikipedia:Verifiability
Non-English sources: 

Citing: Citations to non-English reliable sources are allowed on the English Wikipedia. However, because this project is in English, English-language sources are preferred over non-English ones when they are available and of equal quality and relevance. As with sources in English, if a dispute arises involving a citation to a non-English source, editors may request a quotation of relevant portions of the original source be provided, either in text, in a footnote, or on the article talk page. (See Template:Request quotation.)

Quoting: If you quote a non-English reliable source (whether in the main text or in a footnote), a translation into English should accompany the quote. Translations published by reliable sources are preferred over translations by Wikipedians, but translations by Wikipedians are preferred over machine translations. When using a machine translation of source material, editors should be reasonably certain that the translation is accurate and the source is appropriate. Editors should not rely upon machine translations of non-English sources in contentious articles or biographies of living people. If needed, ask an editor who can translate it for you.
The original text is usually included with the translated text in articles when translated by Wikipedians, and the translating editor is usually not cited. When quoting any material, whether in English or in some other language, be careful not to violate copyright; see the fair-use guideline.

Other issues: 

Verifiability does not guarantee inclusion: While information must be verifiable for inclusion in an article, not all verifiable information must be included. Consensus may determine that certain information does not improve an article. Such information should be omitted or presented instead in a different article. The responsibility for achieving consensus for inclusion is on those seeking to include disputed content.

Tagging a sentence, section, or article: If you want to request an inline citation for an unsourced statement, you can tag a sentence with the {{citation needed}} template by writing {{cn}} or {{fact}}. Other templates exist for tagging sections or entire articles here. You can also leave a note on the talk page asking for a source, or move the material to the talk page and ask for a source there. To request verification that a reference supports the text, tag it with {{verification needed}}. Material that fails verification may be tagged with {{failed verification}} or removed. It helps other editors to explain your rationale for using templates to tag material in the template, edit summary, or on the talk page.
Take special care with contentious material about living and recently deceased people. Unsourced or poorly sourced material that is contentious, especially text that is negative, derogatory, or potentially damaging, should be removed immediately rather than tagged or moved to the talk page.

Exceptional claims require exceptional sourcing: Any exceptional claim requires multiple high-quality sources. Warnings (red flags) that should prompt extra caution include:

Surprising or apparently important claims not covered by multiple mainstream sources;
Challenged claims that are supported purely by primary or self-published sources or those with an apparent conflict of interest;
Reports of a statement by someone that seems out of character or against an interest they had previously defended;
Claims contradicted by the prevailing view within the relevant community or that would significantly alter mainstream assumptions—especially in science, medicine, history, politics, and biographies of living and recently dead people. This is especially true when proponents say there is a conspiracy to silence them.

Verifiability and other principles: 

Copyright and plagiarism: Do not plagiarize or breach copyright when using sources. Summarize source material in your own words as much as possible; when quoting or closely paraphrasing a source, use an inline citation, and in-text attribution where appropriate.
Do not link to any source that violates the copyrights of others per contributors' rights and obligations. You can link to websites that display copyrighted works as long as the website has licensed the work or uses the work in a way compliant with fair use. Knowingly directing others to material that violates copyright may be considered contributory copyright infringement. If there is reason to think a source violates copyright, do not cite it. This is particularly relevant when linking to sites such as Scribd or YouTube, where due care should be taken to avoid linking to material violating copyright.

Neutrality: Even when information is cited to reliable sources, you must present it with a neutral point of view (NPOV). Articles should be based on thorough research of sources. All articles must adhere to NPOV, fairly representing all majority and significant-minority viewpoints published by reliable sources, in rough proportion to the prominence of each view. Tiny-minority views need not be included, except in articles devoted to them. If there is a disagreement between sources, use in-text attribution: "John Smith argues X, while Paul Jones maintains Y," followed by an inline citation. Sources themselves do not need to maintain a neutral point of view. Indeed, many reliable sources are not neutral. Our job as editors is simply to summarize what reliable sources say.

Notability: If no reliable, independent sources can be found on a topic, Wikipedia should not have an article on it (i.e., the topic is not notable).
However, notability is based on the existence of suitable sources, not on the state of sourcing in an article (WP:NEXIST).

Original research: The no original research policy (NOR) is closely related to the Verifiability policy. Among its requirements are:

All material in Wikipedia articles must be attributable to a reliable published source. This means a reliable published source must exist for it, whether or not it is cited in the article.
Sources must support the material clearly and directly: drawing inferences from multiple sources to advance a novel position is prohibited by the NOR policy.
Base articles largely on reliable secondary sources. While primary sources are appropriate in some cases, relying on them can be problematic. For more information, see the Primary, secondary, and tertiary sources section of the NOR policy, and the Misuse of primary sources section of the BLP policy.

See also: 

Guidelines: Reliable sources
Identifying reliable sources (medicine)
Citing sources

Information pages: 

Resources: Backlog – links to articles that need citations added
Template index/Sources of articles – maintenance templates for articles with sourcing problems
The Wikipedia Library – free access to newspapers, journals, and magazines for experienced editors
WikiProject Resource Exchange – where you can ask for help with checking an individual source

Essays: 

Notes: 

References: 

Further reading: Wales, Jimmy. "Insist on sources", WikiEN-l, July 19, 2006: "I really want to encourage a much stronger culture which says: it is better to have no information, than to have information like this, with no sources."—referring to a rather unlikely statement about the founders of Google throwing pies at each other.