"He stole my hat," Laura said.
Notice how the period turns into a comma.
Question marks and exclamation marks
"He stole my hat?" Laura asked.
"He stole my hat!" Laura shrieked.
Notice how the question mark and the exclamation mark remain in the sentence and do not turn into commas.
Moving stuff around
Laura said, "He stole my hat."
Notice the double capitol - both at the beginning of the sentence and at the beginning of the spoken dialogue.
Action after period
"He stole my hat." Laura wiped a tear from her eye.
"He stole my hat." Laura smiled.
"He stole my hat." Laura raised an eyebrow.
Because all these things are actions, they are not a way of speaking and become their own sentences, which means you must end the dialogue sentence with a period, a question mark, or an exclamation mark.
Action stays with the speaker who does the action
"He stole my hat." Laura smiled and pressed her lips to the mirror she held in her hand.
"Oh my!" Jacqueline exclaimed. "Sassy!"
Laura spun, grinning, arms extended, mirror flashing gaslight.
"What is your next move?" Jacqueline asked.
Laura let out a trilling giggle. "Oh, he's going to get it. You'll see."
That's about it. Pretty simple but often messed up. Good luck to all you writers. Keep up the good fight and have fun out there!