Parentheses are used to deemphasize and separate nonessential information from the rest of the sentence—you know, things the writer didn't have to say, but wanted to.
These are called asides. (And yes, Shmoop loves 'em.)
The aside doesn't directly belong; it clarifies something, directs the reader, or speaks to the writer's frame of mind. You could separate asides out with commas or dashes, but the more random they are, the more you should consider using the warm, grammatical embrace of parentheses.
Now that you're on board with parentheses, let's talk about punctuation. If the aside is a complete statement, the terminal, or end, punctuation goes inside the parenthesis, like this:
I have many symptoms. (I'm coughing, sneezing, and itching.)
If the aside isn't a complete sentence, but comes at the end of the sentence, the terminal punctuation goes outside the parenthesis, like this:
I have many symptoms (coughing, sneezing, itching).
What about if the aside is a complete sentence within a sentence? No sweat! Don't capitalize it, and only include terminal punctuation if it needs a question mark or exclamation point. Here's one more example to please the parenthetical gods:
Craig loves (we mean he truly adores) fish.
The aside we mean he truly adores is a complete sentence. Notice that it's not capitalized and, since it doesn't need a question mark or exclamation point, there's no terminal punctuation nestled inside the parenthesis either.