An article on WashingtonPost.com about cartoonists gives an interesting insight into the creative process of one artist, Matthew Diffee. He sits down with a cup of coffee, a pen, some blank paper and starts brainstorming:
"I'll think of something," he says. "I just thought of a barn. What about a barn? A barn raising? Amish people? What about Amish people? They have those beards without mustaches. What would an Amish guy who had a mustache say to a guy who didn't? Those are ideas, but they're not good ideas. So you leave the Amish and you think: corn. And you come up with some bad corn ideas. But maybe one of the bad corn ideas combines with one of the bad Amish ideas and out of the blue, something comes to you."
Here's another example: Years ago, he says, he was thinking about the phrase 'I was in a different place then.' "I wrote down that phrase and I thought, 'How can I make that funny?' " he says. "And months later, I was thinking about pirates: They walk the plank. They have a hook for a hand. Well, what else could they have instead of a hook? You go through the options. It has to be about the size of a hook. You can't use a broom or a canoe paddle. So it has to be a garden tool or a kitchen utensil. And I thought: A spatula is kind of funny." Presto! He drew a pirate with a spatula for a hand and the caption, " I was in a different place then." The New Yorker bought it.
I'd add one tip for this kind of free-association: write down every key word that occurs to you, even if it doesn't lead to a specific idea. For example, in the pirates situation, you'd write down: pirates, walk plank, hook for hand, broom, canoe paddle, garden tool, kitchen utensil, spatula... Even better, make a mind map of all these phrases. Then try different combinations, so your brainstorm process can go backward as well as forward.