For some reason, a lot of native speakers have issues with this, too.

Anytime you use he said/she whispered/he yelled/etc. you'll want to use a comma to separate it from the speech. So:

"Good morning," she said.

"Good morning," she grumbled as she poured herself some coffee.

Use a full stop if you're actually starting a whole new sentence and not just saying WHO your speaker is.

"Good morning." She smiled.

Note that when you use something like, "she smiled" you need to use a full stop since a person can't actually smile dialogue. This is a mistake a lot of native English speakers make.

You can inject the "he said" stuff into the middle of your dialogue, too. In that case, you use commas if you're not at the end of the sentence in your dialogue, and a full stop if you are. Examples:

"Good morning. The meeting will begin," she said and checked her watch, "at eleven o'clock."

"Good morning," she said. "The meeting will begin at eleven o'clock."

I hope that helps. I'm not generally a very good teacher, so if you need clarification on any of that, I'd be happy to take another shot.

*comment edited multiple times because I'm an idiot.