Build relationships with your characters. Funny dialogue comes with complete knowledge of the characters' backgrounds, passions, pet peeves, and even dislikes. Once you have fleshed out each of your characters, place them in various situations and write their perceptions of their environments. Then show the audience the reality of the situation. Comedy lies in the difference between perception and reality. (Think of the character of Michael Scott in "The Office.")
Integrate the funny into your story. An audience wants to follow your character on his journey. They want to become invested in whether he triumphs or fails. Find funny moments along the journey. What happens when your character meets his love interest for the first time? Does he fumble his words, trip over his chair, spill his drink on a grandmotherly barfly, then get back up and resume his conversation as if nothing happened? Perhaps he imagines the two of them in a Bollywood sequence, only to realize he hasn't said a word to her.
Think small. Funny conversations are often about the smallest situations. Deciding whether to paint a room eggshell or antique white, describing an annoyance with gum smacking, or proclaiming the importance of pennies could be the start of a hilarious dialogue. The brilliance of the sitcom "Seinfeld" was that it was seemingly a show about nothing, built on conversations about very small things like "man-hands" and double-dipping the chips.
Study funny scripts. Go to your local library and check out the published scripts from some of your favorite comedies. Deconstruct everything -- plot, character development, even the structure of the joke itself. Sitcom writer/producer Fred Rubin says that you'll often find that the funny word is placed at the end of the joke, and that words ending with a hard "C" or "K" sound give an extra emphasis to the joke. Follow a style that you like, then work to turn it into your own.