Parentheses provide non-essential information in unquoted text. Brackets provide additional information in quoted text.
As with commas and dashes, you can use parentheses to insert some non-essential text into your writing. If the parentheses occur within a sentence, place the final period or comma outside the parentheses and don’t capitalize the first word in parentheses:
I encourage you to watch the show (the cast may be amateur, but they are talented).
The stage director approved of my performance (even though I thought it was awful), but suggested a different costume.
If the parentheses occur within a sentence, place exclamation and question marks inside them, but don’t capitalize the first word in parentheses:
I saw Olivia (is she your cousin?) at the ice rink today
My brother is the head chef at a restaurant that serves nothing but artichokes (yuck!).
When a whole sentence is in parentheses, place all punctuation inside the parentheses and capitalize the first letter:
I applied for a job with Google, but I’m almost certain I’ll be rejected. (Although my aunt’s friend’s cousin works there, so maybe that connection will help.)
Your sentence needs to make grammatical sense without the parenthetical part.
Wrong: Charles (and his dog) are cooking dinner.
Right: Charles (and his dog) is cooking dinner.
Use brackets to insert your own writing into a quotes. They use the same rules of punctuation as parentheses:
Then she said, “I think we should invite her [Lucille], too”.
“It’s like deja-vu all over again [what?].”
If you spot a mistake in the text that you’re quoting, italicize the word sic and put it in brackets after the mistake:
In her essay on Hamlet, May wrote, “‘To bee [sic], or not to be, that is the question.’”
If you change part of a quote, place the change in brackets.
Original: “I say to you today, my friends, though, even though we face the difficulties of today and tomorrow, I still have a dream.”
Changed: “I say to you today, my friends, […] I still have a dream.”
Original: “But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow this ground.”
Changed: “[W]e cannot dedicate, we cannot consecrate, we cannot hallow this ground.”