Our general rule is to avoid brackets as much as you can, but here's some advice when they have forced you into a corner.
Round brackets ( )
Use these when you need to expand on or clarify something:
Or when you're using an acronym or an initialism for the first time:
Otherwise, look for alternatives. For example, in sentences with parenthetical statements – like this one – dashes look much better:
When it comes to using punctuation in brackets, include it before the closing bracket if the complete sentence is in brackets.
Otherwise, punctuate after the closing bracket.
But again, we'd prefer if you got rid of the brackets altogether. Funnily enough, a dash looks better here, too:
Square brackets [ ]
Like their round cousins, try to steer clear of these. Only use them for comments, corrections, references or translations made by a subsequent author or editor:
Angle brackets < > and curly brackets { }
These are used only for technical purposes. So only use them in the correct context and if you're really sure they're appropriate.