"said" is supposed to be "invisible." As soon as you established the speaking order, you just drop the he said/she said tags. You can sprinkle some action in between if it makes sense. The idea of dialogue is to focus on "what's being said." If the emotions are not coming through without the bellowing, yelling, crying, smiling, winking... (I'm still trying to figure out how to groan a speech...) then your dialogue is weak.
There are exceptions, of course. There are times when you must convey certain things that the situation and dialogue can't be clear, or how something is said betrays what's being said. For example, when the character is whispering or doing something out of ordinary:
"What's the matter?" she said.
He tilted his head. "Shh, be quiet."
"Why are you whispering?" she said under her breath.
"Because someone is listening..."
In this case, hopefully it's clear that both characters are whispering, but we only mentioned that once in a tag, to make sure the readers know she's whispering, too.
"I hate you. Very much," she whispered.
If you have a 3-way conversation, then the he said/she said would be essential, unless you have three VERY different speech patterns so the readers are not confused.