While there is some wonderful advice in here, this is also a very common and (somewhat) contentious topic.
As others have pointed out, there are essentially three ways of crafting dialogue. The first, is to use 'said'.
"I can't believe you would do that," she said.
Of course, this can become somewhat boring, or monotonous. This is often the place where writers make a very common mistake:
"I just had to. It was funny!" he snickered.
I once had a mentor who put it like this: people don't laugh things, they don't chuckle things, or smile them, etc. They say things. Everything else is a beat. In simplest terms, a beat is an action. With my students, I love to use an example like this:
"Get out of here," her cheeks flushed red she found the nearest plate and threw it at the wall next to his head. "I said get out!"
The idea here is that we show more depth to what is happening by showing our readers the emotion versus just telling them. By using beats, our readers are pretty well aware that she likely isn't saying these words calmly, or chuckling, or anything like that. She is yelling, she is angry, and whomever "he" is likely did something to upset her.
Part of the effectiveness of beats comes in our ability to paint a picture with the actions of the characters, and not just their words. Beats can quickly become ineffective when they are just being used in place of said. While characters rarely just stand there talking, it is possible. More importantly, when was the last time you held a conversation and did something every time you spoke? Our goal is to emulate natural conversation as much as possible while still telling a story. Embellish a bit, but not so much that we are making our characters feel fake.
Also note that adverbs rarely, if ever, will hold a place here. Many writers (whether this opinion is high brow or not) regard adverbs as lazy writing. This is generally due to the fact that a description of the action is far better than telling your reader how the action was taken.
He rolled out of bed with his legs still limp as they met the floor. The alarm clock was on the ground, shattered to pieces, and his torso was wrapped in a dual-blanket cocoon.
is much better than
He rolled out of bed lazily.
See the difference? Not to say the first example is great by any means, or that the second example is bad, but show don't tell reigns supreme.
There is a book called "Self Editing for Fiction Writers" that covers this subject, as well as quite a few others, in great detail and it is a fantastic read if you are serious about your craft. I highly recommend it!