When someone says the word "cartoon," what we see in our head is usually cel animation. Cartoons today rarely use the pure cel animation of the past, instead employing computers and digital technology to help streamline the process. Cartoons like The Simpsons and Adventure Time are made with cel animation.
A cel is a sheet of transparent cellulose acetate used as a medium for painting animation frames. It is transparent so that it can be laid over other cels and/or a painted background, then photographed. (Source: The Complete Animation Course by Chris Patmore.)
Cel animation is incredibly time consuming and requires incredible organization and attention to detail. It starts with creating a storyboard to visually communicate the story to the production team. Then an animatic is created, to see how the film's timing works. Once the story and timing is approved, the artists go to work creating backgrounds and characters that fit "the look" they're going for. At this time, the actors record their lines and animators use the vocal track to synchronize lip movements of the characters. The director then uses the sound track and animatic to work out the timing of the movement, sounds and scenes. The director puts this information on a dope sheet.
Next, the art is passed from one artist to another, beginning with rough sketches of the characters in action, ending with that action transferred to cels that have been painted.
Finally, the camera person photographs the cels with their coordination background cels. Each frame is photographed according to the dope sheet that was created at the beginning of the animation process.
Then the film is sent to a lab to become a print or a video, depending on the medium that is required. However, if digital technology is employed, much of the cleaning up, painting and photographing of frames is done with computers.