Parentheses or () are widely used by writers to convey additional information in a sentence. They can be considered as a mild digression from the subject and the information included within it is normally not integral to the sentence. In English writing, however, parentheses are abused left and right, with people placing them at all incorrect places or use them way too much.
On the other hand, brackets or  (which many people confuse for parenthesis) are used mainly in quoted material.
To become a complete writer, you need to learn all the nuances of the language and grammar rules. So here is a primer to using parentheses () and brackets  correctly!
Rule #1 Use parentheses to enclose additional information that is not too important to disclose
E.g. The student answered (after 10 minutes) the teacher that he did not understand the subject.
Rule #2 If some information ends a sentence then the period is included after the parentheses
E.g. I received a handsome bonus (INR 60k).
Rule #3 When a complete sentence is written within the parentheses then a period should be used.
However, there have been instances where a sentence is used without a period.
E.g. Please read the report. (You will be shocked.)
Please read the report (you will be shocked).
#Rule 4 Don’t use a comma before or after a parentheses. The sentence should be such that it should read in a flow without any commas if the parentheses is removed.
E.g. Use a fountain pen (a good one from Parker would work well) for the report.
If you remove the parentheses, it becomes ‘use a fountain pen for the report.
Note: Commas are used after the closing parenthesis only if the sentence really requires it.
A bracket allows a writer to correct mistakes, add explanatory information, edit a quote to fit in a sentence, or stress on a word through bold or italics. Like the parentheses, brackets cannot change the meaning of the quote.
Rule #1 Brackets are considered as interruptions. They are mostly added by someone else to explain or comment on the quote.
E.g. Donald Trump shook hands with [his son] Eric.
Rule #2 When a quoted material has some spelling or grammatical mistake or the text sounds confusing, then the term sic is used in italics with non-italic brackets (unless the text is itself in italics).
E.g. The wrestler said, “I would rather retire then [sic] fight with my teammate.
In the above sentence, the use of sic indicates that then was used erroneously instead of than.
Rule #3 Brackets are also used to translate a quote, indicate a change in capitalization, remove objectionable content etc.
E.g. “The first question that the foreign exchange kid asked was qu’est-ce que c’est [What’s going on]”
The military instructor commanded the recruits to “get their [expletive] moving.”