Using she said or he said is sufficient to keep your reader on track with who is speaking each line of dialogue. Often, even these attributions aren’t needed.
Resist the urge to explain. (Don’t do the following):
“You are the apple of my eye,” he said, lovingly.
“And you are the mango of mine,” she said, playing upon his words.
“Shut up!” he shouted angrily.
Often, there is no need to use attributions:
Hanna stepped into the used bookshop and a bell above the door jangled. The smell of dust, mildew and crackled leather tickled inside her nose. She suppressed a sneeze.
“Mein gott, look who’s here.” A white-bearded man wearing a yarmulke and a black overcoat stepped from the behind the counter. “I haven’t seen you in years. You look just like you did—only much more beautiful.”
Hanna glanced around. No others in the store. “Uh… I think you have me confused with someone else.”
“Hanna. You’re Hanna Bernstein.”
She studied the man’s wrinkled face. He reminded her of the white-haired senior rabbi from Beth Yad Vashem, where her grandfather had studied Kabala. But that old scholar was long dead, surely. He’d been ninety-something back when she was riding her bicycle to the school to accompany her grandfather home.
The man smiled at her with a gleaming set of teeth. Not dentures.
“I’m sorry,” she said, “but I can’t remember where we met.”
“I taught your grandfather—blessed be his memory—the mystic Kabala. You remember me, dear. Rebbe Karlbach.”