Dialogue can make or break a story. It is one of the most powerful tools you have if you know how to write dialogue effectively. Here are some of my suggestions. 

Cut to the chase
Every single word of dialogue needs to reveal something about your character's intention or personality. Be brutal, and cut needless words. Obviously you wouldn't want the dialogue to read like a newspaper report, but see how much you can remove, whilst making the same point.
For example:

“What do you want to do this Sunday? I thought we could go to the park.”

“I was thinking about renting a boat,” Sheila said. “Out on one of the lakes.”

“Oh, Shelia, that sounds wonderful! I’ve never gone rowing before.”

That doesn’t mean all your dialogue has to be abrupt, just cut the dead wood. It will flow better and add much more power.

Reveal the backstory of the characters
I believe entwining a character's backstory through dialogue is the most effective way to keep your reader engaged. Hinting that some incident is going to occur, that will require a payoff later in the story, is also powerful. Layering in backstory via dialogue helps keep your reader engaged.
For example:

As they drove toward the house, Carlos muttered, “Can we not bring up Carol again?”

Mary glared at him. “Believe me, I don’t want that any more than you do.”

“Good,” Carlos said. “I mean—”

“Can we not talk about it anymore, please?”

Any reader would assume the subject of Carol will arise at some point. They will wonder who Carol is, and why the subject is so sensitive, so they would stay with the story until that conversation happens. As the story progresses, you could reveal more and more about Carlos’s past and the state of his relationship with Mary. Did she play a part in the relationship between Carlos and Mary? Or was she an innocent bystander? This will offer great opportunities for setups, and help you avoid those awful cliched flashback scenes. 

Reveal Characters' personality
Your reader can learn a lot about your character through dialogue and will help you to 'show not tell'. Please do not tell your reader the character is sarcastic, humourous or cruel, this is annoying and insulting to the reader. You can simply show any personality traits by how they interact with others and the tone they use.

Subtle dialogue
There are many ways you can understate dialogue which brings powerful results.

1. Subtext—where your characters say something other than the true meaning.

Penny falls in love with the older boy next door, who doesn't even know she exists. When she gets to high school, Brian is already captain of the football team, and dating the beautiful head cheerleader, he ignores Penny. When Brian leaves for college, word soon gets back to Penny during her senior year of high school that he and the cheerleader are no longer together. So when Brian comes home after his freshman year of college, Penny just happens to walk outside and notices Brian cleaning his car. She bravely strikes up a conversation with Brian, and he looks up, shocked. Who is this beautiful girl? Is this little Penny from next door?

She says, “Cleaning away the mess, are you?”

Brian looks at the car, and back at her and says, “Yeah, I actually need to clear away a lot of mess out of my life.”

Penny says, “Well, I’ve heard that making a fresh start can be a good thing.”

And he says, “Yeah, I’ve heard that too.”

That’s a quick example of a subtext. Neither character is saying what they really mean. They’re not really talking about cleaning a car, are they?

2. Sidestepping

This is when a character responds to a question by ignoring it and says something completely off-topic. 

In the movie Patch Adams, the late and brilliant Robin Williams played a young doctor who believes the statement in the Old Testament, that “laughter is the best medicine.” In the children’s cancer ward he wears an inflated surgical glove on his head, making him look like a chicken. He wears bedpans for shoes and marches about, flapping his arms and squawking, imitating a chicken. The children laugh and the entire mood of the ward lifts, but hospital directors consider it unprofessional and demand he stops. Patch is trying to make one girl, in particular, laugh. But while everyone else thinks he’s funny, she never smiles.

One day, Patch follows her outside. He says, “I’ve got to ask. Everybody thinks I’m hysterical, but you. I’ve tried everything. Why don’t you ever think anything I say is funny?”
After several seconds, she says, “Men have liked me all my life, all my life…” And we realize by those three words and the tone she uses, she was abused as a child.

Suddenly, the penny drops and we get the reason this girl acts the way she does. She doesn’t trust men, and she doesn’t laugh, because life isn’t funny. But she had not really answered his question. Her problem had nothing to do with him or his humor.

3. Silence
Silence truly can be golden. One of my favorite quotes is from  Abraham Lincoln, “Better to remain silent and be thought a fool than to speak and remove all doubt.”

One of the toughest things to learn as a writer is to avoid filling silent gaps. The same rule 'show don't tell' goes for dialogue. There is no need to tell the reader that someone is silent, or didn't respond to a question. 

For example:

“Well, John,” Babs said, “what do you have to say for yourself?”

John clenched his jaw and stared out the window.

“I’m waiting,” she said.

He lit a cigarette.

Babs shook her head. “For goodness sake, John, honestly.”

It is tempting to add that John didn't respond, or John didn't answer. Don’t!  The reader gets it, and it’s loud, effective, silent dialogue.

Saying nothing, John is actually saying everything.

Read Your Dialogue Out Loud
By reading your dialogue out loud, it will give you the certainty that it flows naturally. Anything that doesn't sound right to you will not read right either. That's when you know it is time for a rewrite until it does.