The best tip I've got is: Pay attention! Start by listening to real conversations. And really listen, too. Note patterns of speech, dialect, how often people are interrupted/talked over, etc. You'll be surprised by how weird conversation is. People laugh at their own jokes, interrupt themselves, repeat words, change the subject suddenly, and interrupt others.
Listen to conversations on TV. Make note of what sounds natural to you, and what doesn't. Does it sound normal when a character repeats another character's name during random bouts of dialogue? That's one thing I noticed immediately when I was trying to improve: people don't call each other by name very often. Certain people do, but most of the time, people will go through an entire conversation without ever saying the other person's name! It's strange, but a quirk that most people share. Stilted dialogue on TV often has characters constantly saying names, while TV that flows well does not.
Now pay attention to dialogue in novels. How does conversation look on a page? What do you think the difference is between good dialogue and not-so-natural dialogue? A few things that jump out to me when I compare dialogue techniques are how much white there is on a page. If there's a rapid back and forth between characters, and there are long blocks of dialogue, then chances are it starts to feel kind of stilted. Most people don't make speeches when they speak. A few people do, but most times they get interrupted before they finish. Another thing I see a lot is extremely clever characters coming up with snappy retorts at an instant. There's nothing wrong with a quick, witty character –but if all your characters are like that, chances are, it's going to feel awkward to read.
One last thing: Don't info dump! If your character is always saying something helpful and informative, and speaks like a history book, then you might have an exposition character. Characters are people, and people suck at explaining things. People who take too long to explain things get interrupted with a lot of needless questions. Keep that in mind when you have a wise character attempt to explain things to less wise characters.
After a while, it starts to feel intuitive. It can be difficult at first, but the key is to pay attention to all the conversations you hear/read. To sum it up: TL;DR, 1. Let characters interrupt themselves and others, 2. Avoid long blocks of dialogue, 3. Don't make all your characters witty, 4. Keep names out of the dialogue as much as possible, and 5. Don't info dump.
Good luck! I hope I helped a little.