The big idea
The four basic rules of punctuating dialogue will solve most of your dialogue-writing problems. Occasionally, however--and I emphasize occasionally, because this will be stuff that you only want to do every once in a while--you can spice your dialogue up a little by setting it up a little differently.
How to do it
Sometimes you can use actions to attribute quotes instead of "he said" phrases. If one of the speakers does something before talking, and if you keep that action in the same paragraph as the quote, then we know that it was that particular character who was talking:
"What's wrong?" Mr. Klingensmith asked.
"Nothing," said Billy.
"Then why are you crying like a little baby?" Mr. Klingensmith asked.
Billy wiped his eyes. "Stop making fun of me!"
. . . .
"Aren't you a big Hannah Montana fan?" Ali squealed.
"No, I'm not," Mr. Klingensmith growled.
"But everybody loves Hannah Montana!"
Mr. Klingensmith spit in the dust. "That's what I think of Hannah Montana."
If the speaker is obvious, sometimes give no attribution:
"Why did I get an F in spelling?" Pete asked.
"Because you failed all your tests," Mr. Klingensmith said.
"But I got an A on the last one!"
"No, you didn't. I just wrote an A to be mean," Mr. Klingensmith chuckled.
Remember that you only replace periods with commas if you have an actual "he said" phrase:
wrong: "I think you're cute," Brianne hugged the puppy.
right: "I think you're cute." Brianne hugged the puppy.
could be written as: "I think you're cute," Brianne said, hugging the puppy.
. . . .
wrong: "Stop talking in class," Mr. Klingensmith shook Pete.
right: "Stop talking in class." Mr. Klingensmith shook Pete.
could be written as: "Stop talking in class," Mr. Klingensmith said, shaking Pete.