Watch plays, movies or TV shows, which are much more dialog dependent than Books. Quinton Tarrentino films are noted for their use of dialog, as are Joss Whedon shows and films (I highly recommend Firefly and Avengers as great examples of his work). Another film example is "Hot Fuzz" which derives a lot of it's humor from the use of dialog. Archer, is another show which has almost entirely dialog based humor. Several times an entire plot line will consist of only dialog based humor, and almost once a season, the transitions from the A-plot scenes to the B-plot scenes are done in such away that the first line in new scene would fit in naturally with the last line of the previous scene... despite being part of a different conversation on a different topic entirely. For kids shows, I recommend works created by Greg Weisman.
Unlike others on this page, I contest that dialog is "tell" as opposed to "show" as dialog is an action. What someone says... and more importantly how someone chooses to say it can inform an amazing detail of their characters in subtle ways that prose cannot.
Dialog is one of the chief ways to get ideas out to the audience as dialog can often convey dramatic changes or demonstrate a character's thoughts.
One trick to do with a dialog scene (or any part of the story) is to work your way backward from finish to start. When the conversation is over, what do you want the readers to take away. Why is it important. What is being said, and why does it need to be said for the story to work.
I should also be stressed that with dialog, unless it is important to be said in that particular way, is rarely grammatically perfect. People do not talk with grammatically perfect dialog. Never let perfect dialog be the enemy of good dialog. Get used to those squiggly red lines to show up when writing dialog drafts, because it's going to happen. Especially if you do phonetic spelling to show a character using an accent. People mispronounce things all the time. And lots of people use "Me and someone else" as a subject. Whatever rules you have about proper writing, lose them for the dialog. (If you do do a phonetic spelling for characters with accents, try to avoid making it read so thick that you can't understand what they're saying. It usually easier to listen to... say... a person with a Scottish Accent than read a Scottish Accent...).
I also recommend thinking of dialog from the point of view that you are writing a script (with stage descriptions) rather than a novel. In conversations, what will the audience see and hear? You may even want to block the scene out, especially if the dialog occurs in a fast moving scene (blocking being the stage turn for choreographing the movement and timing of the actors through a scene on the stage). In novel writing, it's often hard to forget the environment that you're in and that a critical component of dialog is body language and tone. Consider the following sample dialog:
"No. Stop. Don't," he said.
Which doesn't tell you much about the character's state of mind when he said the lines. Was he trying to warn someone who was about to do something dangerous to cease the actions? Or was he delivering the lines like Gene Wilder's titular character in "Will Wonka and the Chocolate Factory" where he already knows the person who he's warning is going to do the dangerous thing no matter what he says and is only going through the motions of telling the kid not too, even though by now he's lost all the emotional panic one should have in the scene. The use of punctuation (Exclamation points) and a description of the tone of voice and the body language will tell you as much as the dialog... and combined with each other tells you other things. Essentially Wonka has decided not to do anything beyond what he is obligated to do because if the fates of the previous children haven't taught this brat that maybe you shouldn't mess around with strange things in the factory, what's one more panicked voice going to do.
The point is, dialog does not occur in a vacuum, and that many writers will forget this if they are not working in a visual medium (i.e. Books and short stories).
Also don't be afraid of the word "said" and avoid other dialog tags in favor of describing the manner dialog was said with adverbs or additional adverbs modifying the character's speaking voice. If the character does something while they say something, but dialog paragraphs should either start with the quote, end with the quote, or start and end with the quote ("I wonder," Tom said to no one in particular, "If this would work.")
Again, act out your dialog in a space that can represent the environment. Step through the conversation with your goal and the other speaker's goal in mind. If you think you can give a fair voice to both characters, do it your self. If you can't ask a friend... set the scene, explain the pov they're acting out, the space, and ask them to respond accordingly. See what the friend thinks the appropriate response is... it could be more authentic... hell, it might be funnier than what you thought.
If the space isn't private but accessible to you, go there and work out the scene yourself... don't worry about what strangers will think and if they ask, well, you'd be surprised what people will let you get away with if you tell them "It's for a book."