Keep in mind: If the item you are citing is itself a citation of another source, as many social media posts are, find and cite the original source, not the retweet or linking item.
Basic Format
APA
Twitter user name. (Year tweet was posted, Month Day). Full text of tweet [Twitter post]. Retrieved from Twitter Account's URL
Chicago
Lastname, Firstname [or single username] (@handle). Year. "Full text of tweet." Twitter, Month day, year, time posted. URL.
MLA
Twitter Handle (First Name Last Name if Known). "Full text of tweet." Twitter, Day Month Year of Tweet, Time of Tweet, URL.
Example
APA
@NASA. (2019, April 10). In a historic feat by @EHTelescope & @NSF, a black hole image has been captured for the 1st time. Several of our missions observed the same black hole using different light wavelengths and collected data to understand the black hole's environment. Details: https://go.nasa.gov/2Uwj1PF. [Twitter post]. Retrieved from https://twitter.com/NASA/status/1115973963358834689.
Chicago
National Aeronautics and Space Administration (@NASA). 2019. "In a historic feat by @EHTelescope & @NSF, a black hole image has been captured for the 1st time. Several of our missions observed the same black hole using different light wavelengths and collected data to understand the black hole's environment. Details: https://go.nasa.gov/2Uwj1PF." Twitter, April 10, 2019, 9:45 a.m. https://twitter.com/NASA/status/1115973963358834689.
MLA
@NASA. "In a historic feat by @EHTelescope & @NSF, a black hole image has been captured for the 1st time. Several of our missions observed the same black hole using different light wavelengths and collected data to understand the black hole's environment. Details: https://go.nasa.gov/2Uwj1PF." Twitter, 10 April 2019, 9:45 a.m., twitter.com/NASA/status/1115973963358834689.
Facebook Post or Page
APA
Post from individual
Author, A.A. [Authorname]. (YYYY, Month Day). Content of post up to first 40 words, or description if image or video [Facebook status update]. Retrieved from http://www.RetrievalURL.com.
Tyson, N.D. [Neil deGrasse]. (2019, April 22). For me, every day is #EarthDay [Facebook status update]. Retrieved from https://www.facebook.com/neildegrassetyson/posts/10157217769171613:0
Page from group/institution
Big Company. (YYYY). Description of page [Facebook page]. Retrieved Month Day, YYYY, from http://www.RetrievalURL.com.
American Library Association. (n.d.). Timeline [Facebook page]. Retrieved April 22, 2019, from https://www.facebook.com/AmericanLibraryAssociation/
For more detail, see How to Cite Social Media in APA Style.
Chicago
Authorname A. Author, "Text of post up to 160 characters," Facebook, Month Day, YYYY, http://www.RetrievalURL.com.
1. Neil deGrasse Tyson, "For me, every day is #EarthDay," Facebook, April 22, 2019, https://www.facebook.com/neildegrassetyson/posts/10157217769171613:0.
or, in bibliography:
Tyson, Neil deGrasse. "For me, every day is #EarthDay." Facebook, April 22, 2019. https://www.facebook.com/neildegrassetyson/posts/10157217769171613:0.
See 14.209: Citing Social Media Content.
MLA
Author, Authorname. Description of Post. Facebook, Day Month YYYY of Post, Time of Post, URL. Accessed Day Month YYYY.
Tyson, Neil deGrasse. Earth Day acknowledgment with photo of Earth from space. Facebook, 22 April 2019, 8:29 a.m., https://www.facebook.com/neildegrassetyson/posts/10157217769171613:0. Accessed 23 April 2019.
Each citation format will require some or all of the following information: the Instagram account holder’s name, if known, and/or username; photo title or description*; names of any other contributors (i.e., an original photographer if the Instagram poster did not create the image); the date the photo was published on Instagram; the date it was accessed; the photo's Instagram URL.
*If there is no title, a short description will suffice.
APA
Last Name, First Initial or Username (Year, Date Published). Photo title [Photo description]. Retrieved from URL
Chicago
Lastname, Firstname or Username. “Photo Title.” Instagram, Date published. Date accessed. URL.
MLA
Lastname, Firstname or Username. “Photo Title or Description.” Instagram, Other contributors, Date photo was published, URL
With Instagram, it is very common for an image to be reposted from another source. If the original source is available, cite the original source rather than the Instagram post. You might be tempted to cite this image as
@nypl (2019, April 17). [Photograph of four women, one in fancy dress]. Retrieved from https://www.instagram.com/p/BwXx_vCFIOn/?hl=en
However, you should use the information given in the post to find the source in NYPL's digital archives:
Manuscripts and Archives Division, The New York Public Library. (1935-1945). Amusements - American Jubilee - Performers - Ermine Hawthorn and women. Retrieved from http://digitalcollections.nypl.org/items/5e66b3e8-b625-d471-e040-e00a180654d7