The said rule is two-folded. On one hand, a conversation that looks like...

[i]"I like peanut butter." said Jim.

"That is good. I like jelly to be in my mouth." said Lisa.

"I like a lot of things in my mouth too." said Jim

"We should be friends for a while. And maybe we can eat peanut butter." said Lisa

"And Jelly." said Jim[/i]

...gets really tedious really fast. On the other hand, if it looks like...

[i]"I like peanut butter." enunciated Jim.

"That is good. I like jelly to be in my mouth." Lisa warbled.

"I like a lot of things in my mouth too." sighed Jim.

"We should be friends for a while. And maybe we can eat peanut butter." roared Lisa.

"And Jelly." added Jim.[/i]

...it's still tedious. It is good to practice not overusing words, [i]said[/i] included, but [i]said[/i] does have its place. If somebody says something in a normal way, or in a way that isn't worth drawing attention to, and you still need to specify who is speaking, then [i]said[/i] has its place. What you want to do is mix up sentence structure so that you don't fall into a monotonous pattern. Also, it is a good idea to drop the speaker indicator when you can. And, of course, it's always good to be descriptive, and a good descriptive dialogue indicators can set the tone for the rest of the conversation so that you no longer need them.

So, for me, a good dialogue looks like

[i]"I like peanut butter." said Jim.

Lisa's eyes lit up and, like a child, she pointed wildly at her open jaw. "That is good. I like jelly to be in my mouth."

"I like a lot of things in my mouth too." 

"We should be friends for a while. And maybe we can eat peanut butter."

"And Jelly." Jim added, giving Lisa a hearty thumbs up. [/i]