Quotation marks are very useful punctuation marks, but the grammar rules that come with them are complex and numerous.
Let us start with the basics. Quotation marks are used to indicate that a particular piece of text has been taken from another source. They also indicate when a character is speaking — they convey dialogue. "Salutations! How are you doing today?" asked the boy.
When there is a quote within another quote, you use apostrophes rather than quotation marks for the inner quote. "He said, 'I don't think so,' but it wasn't any use. She didn't believe him."