Show a situation where what happens is the opposite of what you'd expect: a chicken frying food or a person taking clean clothes to a laundromat. Exaggerate or distort the truth: the athlete is so thirsty he drinks an entire swimming pool. Show a humorous sign on the wall in an office, or a strange traffic sign.
Gag cartoons often stand alone, so it's not as important to develop characters as it is with strip cartoons. Still, your cartoons will develop a following more readily if you have a recognizable "look" to your cartoons. You will also find them easier to draw if you rely on a repertoire of settings and characters, instead of inventing a new one for each cartoon.
Most gag cartoons are one-panel cartoons, though they can be short strips as well. Either way, plan out where the elements will go. If you have characters speaking, the balloon is usually above the speaker. But if you have a conversation in a single panel, put the first speaker's balloon at the top and the second speaker's at the bottom.
Draw in pencil and then ink it over with a pen. Neatness especially counts in lettering. If you are not satisfied with your handwriting, use a computer font that looks like hand-printed letters. Use the same font, same thickness of ink, and the same size and shape panel.
A simple cartoon is often the best choice. Don't spend time on extraneous background elements that don't have anything to do with the joke. Pinpoint the main idea and concentrate on that.
Seek out libraries and bookstores (especially larger ones) for books on cartooning and gagwriting. Pay attention to what makes things funny in other media: You may be able to translate a joke from a TV show or even a commercial into a great cartoon. Don't limit yourself to modern creations; older shows and cartoons that are no longer popular have some great jokes that today's audiences have not seen but may enjoy if you bring them back in an updated form.
After you write a gag, leave it alone--for at least an hour; overnight is better. After your break, read it again with fresh eyes to find errors and to see if it's really funny. You may find yourself rewording your gag to make it more clear or give it more punch.