Dialogue comes naturally to me as a writer, maybe because I started out being interested in acting and took that to my role-playing, but even my childish note books with my scrawled scifi story has those tell-tale quotes. Now that I think about it one of my first completed pieces of writing was actually a play with hefty dialogue between the three characters. Now I wonder where I stashed that little gem?
I can literally hear my characters speak and I pick up on their cadence and rhythm. In fact if I can't hear a character speaking out loud in my head I know I'm in trouble with that character. They are not yet alive in my imagination.
My characters talk and jabber at me and I quite often run long monologues in my head from my particularly vocal characters. I have a friend who considers her own inner character monologues to be a form of channeling, and it may be. After all where does inspiration come from? The Muses?
Once I sit down to write a scene though the dialogue must not become a monologue however. It must reveal something about the story, conceal others if I'm still trying to keep my readers guessing, and it must interact with the other characters, even if they are only actively listening. The voice of my characters each must be distinct. It should be fairly clear who is talking even if you removed every tag, every reference to action outside of the dialogue.
For instance much of the plot of The Postman Always Rings Twice by James M. Cain is propelled by dialogue and little of it is tagged, yet the voice of his characters is so real and distinctive, each voice clear as a bell, that you know who is talking. And Cain does not write "he said" or "she said" either. I'm not sure, because I haven't read it in years, but I'm pretty sure if you counted you wouldn't find an example of either in the entire quick and explosive novel. He doesn't replace 'said' with adverbs or with other possibilities like 'growled, yelled, barked,' or 'throatily'. He lets the dialogue and the spare description do the work.
I'm now going to suggest something outrageous in the history of writing how-to tips: throw away the damned thesaurus. No good comes of a thesaurus. I have probably been guilty as hell in previous writing pieces in suggesting that people look for different words to say the same thing, but what you really need is to cultivate a love of words so that they are handy in your head, not fake it by grabbing the thesaurus. Do not, please I beg you, write 'amber liquid' instead of 'beer'.
Back to dialogue: actually never do the preceding when writing dialogue unless the character is some kind of odd pedant with a penchant for thesaurus cruising and then peppering his speech with oddities. Do clip out all unnecessary tags when possible. Leave just enough to indicate who is talking at the beginning of passage of conversation. Occasionally you will have call to write a little description of what the characters are doing, but keep it spare and keep it important to the dialogue and to telling the story.
From The Postman Always Rings Twice:
"He suspicions us, Frank."
"It's the same one, he knew there was something wrong, soon as he saw me standing there, keeping watch, he still thinks so…"
"What are we going to do?"
"I don't know. It all depends on the stepladder, whether he tumbles what it's there for. What did you do with that slug, shot?"
"I still got here in the pocket of my dress."
"God Almighty, if they had arrested you back there, and searched you we'd have been sunk."
I gave her my knife, cut the string of the bag, and take the bearings out. Then I made her climb back, raise the back seat, and put the bag under it. It would look like a rag, like anybody would keep with the tools.
"You stay back there, now, and keep an eye on that cop. I'm going to snap these bearings into the bushes one at a time, and you've got to watch if he notices anything."
It's quite clear who is speaking. Cain starts us off in this passage with the name 'Frank' and goes from there without any other indicator but the order of the line and tone of voice. The description is spare and to the point. It serves the story. She doesn't flick her auburn locks out of her eyes and give him a pert but 'knowing' look with her emerald eyes.
Of course not everyone writes like Cain nor should they. Your own style and unique voice is essential, but the basic principles of good writing are: show us, don't tell us, and keep all the words, even the dialogue and description, in service of the plot.