Is there a rule for punctuation with quotes? When does punctuation go inside or outside the quotation marks of the word it follows?

If the sentence ends with a quote, the period goes inside the quotes.

If a sentence has a quote that ends the sentence, the period would go inside the and you don't need one outside. This applies even if the statement you are quoting isn't the end of a sentence. Such as, you are quoting, "dogs can be very helpful, and joyful" and want to put in a sentence. It would look like, I want a dog because, "dogs can be very helpful."