A quote within a quote is set apart with single quotation marks -- ' as in this example:
"She's horrible. Always nagging at me. Telling me what to do. Why just yesterday, she screamed at me. 'You're a worthless little thing.' That's exactly what she said."
If you're surrounding dialogue with action or emotion, always use a period at the end of the dialogue:
"She's horrible. Always nagging at me. Telling me what to do." Paulette brushed a lock of hair away from her eyes and sank into the chair. "Why just yesterday she screamed at me. 'You're a worthless little thing.' That's exactly what she said."
unless you're using a dialogue tag and/or a gerund phrase, in which case you'll use a comma:
"She's horrible," Paulette said, brushing a lock of hair away from her eyes and sinking into the chair. "Always nagging at me. Telling me what to do. Why just yesterday she screamed at me. 'You're a worthless little thing.' That's exactly what she said."
Whenever you use a comma to set off dialogue, you're signaling the reader that you're using some kind of tag to modify the dialogue. A cue as to the tone of voice used to say whatever has been said. If you punctuate the dialogue incorrectly, you'll pull readers out of the moment while they try to follow what you're saying. The more often you do that, the more you weaken your story.
And on the subject of tags, if you must use them--and we all do from time to time--keep a few things in mind.
In spite what seems to be an on-going love affair with the tag "hiss," no one can hiss a sentence without at least one S in it. "You're a creep," she hissed is physically impossible, and because it is, it's irritating to many readers.
If you're going to have someone grind out a few words between clenched teeth, keep it to a few words. It's believable that someone might say, "She's horrible!" from between clenched teeth. But it's very difficult to believe that anyone's teeth could remain clenched for two or three sentences at a time.
Writing something like this:
"Oh, Jonathan. You are by far the kindest, gentlest man I've ever met and I adore you," she laughed.
Is very likely to irritate readers. Try saying that much while laughing the entire time. Unless you're made of something I'm not, you just can't do it without sounding ridiculous or your laughter sounding false. Here again, about the most anyone can do is to laugh while saying a word or two. Maybe three. Far better to write it this way:
"Oh Jonathan." She laughed and touched his hand gently. "You are by far the kindest, gentlest man I've ever met and I adore you."
When you're reading the dialogue, you'll probably find yourself making the changes aloud that should be made to the page. Read it with a pen handy so you can mark what needs to be revised. You'll be amazed by the results.