Bracket placement

My idea of using of various brackets is unclear; can anybody clarify as to where exactly I use () and []? Furtermore, are {} used in regular grammar?

Solution 1:

Parentheses are used to indicate, well, parenthetical thoughts.

We discussed the value (or lack thereof) of homeopathic medicine.

Square brackets are used to indicate alterations, omissions, or supplementary material in quotations.

I believe it was Thomas Paine who said "These [the years leading up to the American Revolution] are times that try men's souls."

I cannot think of a use for curly braces in ordinary writing.