Avoid using too many brackets in text and make sure they are always closed. If the whole statement is within brackets the final full stop should be inside them.

Use round brackets when adding supplementary information to the text.

The arithmetic was wrong (which is unheard of)
The Royal Society for the Protection of Animals (RSPCA)
(The Authority has the final say on these.)

Use square brackets when adding comments or corrections.

The judge stated: “You [Mr Sykes] have suffered.”
On Twitter she said: “The statistecs [sic] seemed wrong”

Avoid having two brackets next to each other. Use one set of brackets and a comma or semicolon to separate the information.

(up 22% to 79,117 offences; Figure 13)
…as shown in the data (Figure 12, Table A1)

Also try to avoid brackets within brackets unless it is an acronym that you need to provide.

…as shown in the data (Annual Business Survey (ABS))