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Comic book dialogue is a bit of a strange beast. There are punctuation rules in comics that are different from prose, and as a creator, you should be aware of them. I'm going to speak in generalities, and then give exceptions to these rules afterwards.
First, there are no quotation marks around the dialogue in word balloons. I know that new writers are used to putting them in because they're used to writing prose. Don't. A comic script is more akin to a stage play, and there's none there, either. If you put in quotation marks, you're only going to cause your letterer to do more work. No one likes doing extra work when they shouldn't have to.
Second, most of the time the dialogue will be put into an all-caps font by the letterer. I say this because most of the time it won't matter if you write in all caps or if you write using sentence case, but if you write in all caps, make sure you change your spellcheck settings in order to check your dialogue, too. Remember, dialogue is the only thing the reader is going to see; spelling mistakes creep in easier using all caps than they do in sentence case.
Most of the time, you only need a comma, a period, a question mark, and an exclamation point. Sometimes you need an interrobang. (Don't know what that is? Time to do some research!) Generally, you don't need to use a semicolon or a colon.
The double-dash is a different thing, though. This is generally used when a character is interrupted in their speech. It has to be a double-dash, not a single one. And you have to be careful when using the double-dash, because most word processing programs will change the double-dash to an em-dash. You have to go back in and convert it. (A bit of trivia: an em-dash is a long dash, and the double-dash will convert to an em-dash if you write a word directly after the second dash. An en-dash is a single dash. They are called these because in theory, they took up the space of the letters they're named after, depending on the font used.)
Quotation marks are used in voice-over captions when one character is speaking to another, and neither character is in the scene being depicted. This will happen more often than the next use, which is when one character is quoting something.
These rules are easy. Just try to keep them in mind when you're writing.