Example one: too many explicit speech tags.
"I want to go to the park," said Billy.
"Me too!" said Tommy.
"You can't go to the park until you finish your vegetables," said Mom.
"Awww!" said the boys.
"Don't make me say it again," said Mom.
As you can see, nothing but "said said said" gets very old. Swapping out "said" for other words like "asked" or "chorused" only helps a little. This exchange simply has too many explicit speech tags.
Example two: speech tags that are not explicit.
"But Jeffy and Mikey will be at the park at six!"
"They'll be alone at the park all week if this whining keeps up," Mom warned.
"Guess we'd better eat up," the sullen boy grumbled to his brother.
In this example, we don’t know which boy says the first sentence or the last sentence, even though the last sentence has a speech tag. These problems could be fixed by implicit or explicit speech tags; preferably, a combination of both, but the last speech tag needs to make clear which boy is speaking.
In a two person conversation, you can skip speech attributions with more confidence.
Example three: skipping speech tags.
As Mom left the room, Billy leaned over and whispered to Tommy, "Quick! Slip your veggies to Fido!"
"D'you think we should?"
His brother was already dropping carrots on the floor. "Why not?"
"Won't she know?"
Billy gave him a hard stare. "She won't if you don't tell her."
The middle three pieces of dialogue are technically unattributed, but since we know that there are only two people in the conversation, Billy and Tommy, it is easy to follow who says what. However, people usually start losing track of who said what after about three unattributed dialogue changes. Attributions can also be made within the dialogue, such as "I dunno, Billy, d'you think we should?" or "Why not, Tommy?" You may have noticed that written dialogue has a lot more of these included attributions that normal speech does. When you are talking to someone face-to-face, your eye contact and body posture indicate to whom you are speaking even if there are more than two people present. Writers have to make up for the lack of visual cues.