Dialogue tags are not necessary if you only have two people talking. Sprinkle them here and there so that the readers don't lose track after 3 pages of dialogue. It's also about pace. You can have some rapid-fire dialogue to speed things up without bogging them down with tags or action:
"What happened?"
"God knows?"
"How did he died?"
"Beats me."
"What else did she say?"
"Why don't you ask her instead?"
It works well with short dialogue.
I usually just use "said" and "asked." Sometimes I need to clarify the way the character speaks the line because the speech itself is not indicative: "whispered," "shouted," etc. But that's it.
I also use dialogue tags (and sometimes short action) to give it a beat:
"Hey lady," he said. "Get out of my store."
Try not to use exclamation point. Use the tag instead:
"Hey lady," he shouted. "Get out of my store."
Also, real people do NOT speak with LONG, run-on, or grammatically perfect sentences -- that's what we call stilted dialogue:
"Rina, my mother is coming to town today and we must make the house look wonderful and impress her so that she will see that our marriage is not a sham."
Ugh! Instead, try making the sentences short: no more than 5 words, and mess up the grammar a bit as your character would do...
"Rina, my mother is coming to town. Today. Make the house look wonderful. We must impress her. So she knows, our marriage is not a sham."
Better yet, break it up by giving the other character something to response with:
"Rina, my mother is coming to down."
"Today?"
"Yeah, please make the house look wonderful."
"You want to impress her."
"I want her to know..."
"That our marriage's not a sham."
(suddenly, you have characterization and even conflict...)
Action is okay to break up the dialogue, but don't over use it. It makes for a choppy read, and shows down the pace. And if the action is trivial, it gets really annoying (she smiles, she grins, she takes a bite, she gazes at him, she lowers her head, etc. etc.)
And don't get me started on info-dumpy dialogue, when the characters tell each other things they already know so to dump information for the readers:
"My dear wife, Ruth, my mother is coming today. She is 80 years old and she can't see very well."
"I will clean the house. I know she can't move very well either. She has arthritis for 10 years now."
"And make her favorite food, which is chicken with honey sauce."
A knock at the door. John opened it.
"Ruth, see what is here. My mother, Mrs. Pickles."
(shoot the author!)