There are several steps in the making of the Simpsons. This is how it's done :

1. The Script

Of course, when you are making a cartoon, you first need a script...
The script of the Simpsons is written several times (each scene is rewritten about eight times). When the script is complete, there's a table read, which is a gathering of the cast and all the producers so the writers can hear the script out loud and make more changes to it.

2. Recording the voices

When the final script is ready, the voices are recorded. They do this like an old radio play : The cast stands in a semi circle so they can see each other. The voices are recorded before making the drawings because it's easier to do the timing of the animations that way.
Click here to see who does which voice

3. Soundtrack

After the recording of the voices, a soundtrack of 24 minutes is made.This soundtrack, together with the script is then sent to Korea, where the animations are made.

4. The Animation

A. The Storyboard

First a storyboard is made. This is a panel by panel illustration of each scene. The average storyboard contains 200 pages which contain 4 or 5 shots each.

B. Reviewing the scenes

Once the storyboard is made, each scene is reviewed scrupulously. Nothing is left to chance. Everything is carefully gone over by a team of people looking for errors.

C. Creating new characters and locations

Each episode contains new characters and locations. These are designed on a show-by-show basis.

D. Creation of a mini-movie

When the rough drawings have been drawn, they are all shot by a camera which is connected to a computer. On the computer all the images are placed behind each other and a mini-movie of the show is made. This mini-movie is called an animatic.
This is the way the producers see how the animation flows, how the jokes work and if the timing is right.

E. Animation in color

After the making of the animatic, a start is made on the making the final animations. Those are colored with a limited palette.

5. Final

About three months after sending the script and soundtrack to Korea the animation comes back to the writers. The script is sometimes rewritten AGAIN.
The 24 minutes of animation that return from Korea are then cut down to 22 minutes (22 minutes being the duration of the show). Now (after 10 months!) the episode is finally ready to hit the air.