How should brackets be used to add words to a direct quotation?
When additional words written by an individual other than the original author are inserted into a quotation, the added words must be surrounded by brackets. The inserted material should present an accurate representation of the author’s message in the original text.
Let’s look at an example:
Using an excerpt from Marc Kutner’s book, Astronomy: A Physical Perspective, the bracketed words in the quoted sentence were inserted into the quotation to clarify the meaning of the word they:
Original direct quotation: “Since they carry the continents with them as they move, we refer to this motion as continental drift” (Kutner, 2003, p. 451). 
Quoted sentence with added words: “Since they [tectonic plates] carry the continents with them as they move, we refer to this motion as continental drift” (Kutner, 2003, p. 451). 
How should brackets be used to indicate an original error in a direct quotation?
To indicate that an incorrect spelling or a grammar error appears in the original work and that you are accurately reproducing the original material, insert the word sic in italics and enclose it in brackets directly after the error [sic].
Let’s look at some examples:
If a participant in a research experiment incorrectly spells a word in a written response, you might indicate the error in your paper as follows:
In response to the question, “How many hours of sleep per night, on average, do you receive?” one participant reported, “Twevle [sic] hours of sleep.”
In the following example, the synonymous words gaining and obtaining are both included (incorrectly) in a single sentence, leading to redundancy:
As Simonsen (2012) argues, “research should also be valid, verifiable, and unbiased, to attain the overarching goal of gaining obtaining [sic] generalisable knowledge” (p. 46). 
 Kutner, M. L. (2003). Astronomy: A physical perspective. New York, NY: Cambridge University Press.
 Simonsen, S. (2012). Acceptable risk in biomedical research. New York, NY: Springer.