Dialogue is an ideal place for showing in your story. When reading, the dialogue bits pop off the page and readers tend to enjoy them because they move quickly.
Some ideas to improve your dialogue:
Avoid idle chit chat: For the most part, though in real life we may do the: how are you, fine, can't believe how hot it's been, how're the kids...in writing, it becomes tedious and downright boring for the reader.
Streamline: Each line needs to add to your story somehow. The primary purpose of dialogue is to illuminate character. We see them in action by what they're saying and how they react to others. Of course, plot points are revealed through dialogue, too.
Avoid giving speeches: Or having your characters give speeches. Think about how fast you tune out when someone pontificates without you having a chance to respond. That's what your reader will do if you have a long block of speech-giving. While sometimes you need to have long stretches of speech, consider inserting interruptions, questions in order to bring that same speech to life and show your characters' traits.
Leave the grammar police behind: People don't speak in grammatically correct sentences all the time. Use contractions, fragments, and appropriate slang to bring your piece to life. Be careful with the slang though, unless you want to date your piece in the here and now (or some other era) don't overdo it.
Insert appropriate body language: Within your dialogue remember you're painting a picture for your reader. You don't need to do a lot of action during dialogue, and you don't want to direct the scene, but you do want to give color to the scene and your characters by giving them some action while speaking.
Use speech tags: He said, she said are the best. You may have heard, they are invisible, and they are, but they give the reader a point of reference so they can keep track of the speaker. If your conversation is between two people, you don't have to put a tag after every piece of dialogue. If the reader knows who is talking from your situation and how you've crafted your characters, then you can leave the tags off.
Avoid names: Have you ever noticed we rarely use someone's name when we're talking with them directly unless we're trying to make a point or get their attention. The same should be true in your dialogue.
Avoid those adverbs: In most cases including such things like, he said ferociously is telling rather than showing. If he's being ferocious, show it. He bared his teeth. "You have no idea what you just did." - shows us, while "You have no idea what you just did," he said ferociously, tells us.
Change the topic: Keep your reader guessing by having an unexpected twist in the conversation.
Avoid the "As you know, Bob," trap. One of the characters in the conversation needs to not know the story. If they both know what's happening, then it becomes dialogue for the purpose of giving the reader information and it reads fake. Consider Sally speaking with her husband, Bob. "You know, Bob, last year when we moved from the city, everything was great for a while. Then we started farming and the storm hit and we lost the crops and the bank took the farm." (If Sally and Bob are talking to one another and went through the experience together, this is