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This will give you an opportunity to hear how it sounds. You can make changes based on what you hear as well as what you read. Allow a little time to go by after you've written the dialogue to read it, otherwise your brain will fill in what you were going for rather than what is actually on the page. Have a trusted friend or family member go over your dialogue. A fresh pair of eyes can tell you whether your dialogue is natural sounding, or needs work. There is nothing more irritating to a reader (including and especially, publishers and agents) than punctuation that is being abused, especially in dialogue.  There should be a comma after the end of the dialogue and the closing quotation mark. For example: "Hello. I'm Jane," said Jane. If you add action to the middle of a piece of dialogue, you'll either capitalize the second half of the dialogue, or not. For example: "I can't believe he killed my father," Jane said, her eyes filling with tears. "It's just not like him." or "I can't believe he killed my father," Jane said, her eyes filling with tears, "since it's just not like him." If there's no said, only an action, then there's a period in place of a comma in the closing quotation mark. For example: "Goodbye, Aunt Agatha." Jane slammed the phone down. Sometimes, less dialogue is more. When people talk, they are not overly verbose. They say things in short, simple ways and you'll want to reflect that in your dialogue. For example, instead of "I cannot believe that after all these many years, it was Uncle Red that put the poison in my father's evening cocktail and murdered him," said Jane, you might say "I can't believe Uncle Red poisoned my father!" Each character should have her own sound and voice, but too much of an accent or a drawl will become annoying or even offensive to readers. Also, using a dialect you aren't familiar with can end up employing stereotypes and being incredibly offensive to the natural speakers of the dialect. Establish where characters come from in other ways. For example, use regional terms such as "soda" versus "pop" to establish geography. Make sure if you're writing a character from a specific geographic area (like England or America) that you use the appropriate slang and terminology (pants in England, underwear in America, for example).
Read your dialogue out loud. Punctuate your speech correctly. Cut out any unnecessary words or phrases. Use dialect carefully.