Step 1: Supplies
Material - Both fleece and something that's not fleece that you could easily screen print onto. But you don't have to use the fleece with it if you don't want to.
Fiber fill (A.K.A. Stuffing) - Obviously it won't be a pillow without stuffing.
Paint - Acrylic works well, but fabric paint would be even better. You'll probably want black paint for this.
Paper - Preferably with the quote of your choosing printed on it. Also, some blank pieces of paper for the bottom part when you're making the stencil for screen printing and then some more for the stencil of the thought bubble.
Printer - To print on the paper with.
Garbage bag - Makes the paper stick to the material.
Iron - You might want to iron your material, and also you need it because it goes with the garbage bag and since the garbage bag goes with the paper the iron also does.
Sewing machine - You probably won't want to sew all this by hand.
X-acto knife, paintbrush, scissors, stuff to write on the material with, all those other small things you might need - Obviously, you're going to need stuff like scissors and x-acto knives and who knows what else.
Step 2: Choosing a Quote
So when you're looking for a quote, look one that won't require much cutting of a stencil, and one that makes sense when it isn't actually in the comic.
When I printed it I used size 100 font, but depending on how big your pillow is going to be you should use a bigger or smaller size.
Step 3: Stencil Making
Take a piece of a garbage bag that's about the size of your pieces of paper, and put it between one piece of paper that is printed on, and one that is blank. When you iron the garbage bag between the pieces of paper it will melt so they stick together, and later once you have cut out what needs to be cut out it will be used to stick the stencil to the fabric. Line up the pieces of paper and iron the paper/garbage bag so that the garbage bag sticks to both pieces of paper. Repeat for all the other pieces of paper that you have printed on. Also, now is the time to do that for the paper that will become the stencil of the thought bubble. Just use blank pieces of paper for that though, since you're going to draw it on.
Decide how big you want the thought bubble to be, and use enough paper to make it the size you want. Don't forget to make the little circular parts that are always at the bottom (there's a picture to show what the heck "the little circular parts that are always at the bottom" are). After you have the outline, go back and draw another outline inside of the first one you drew (both on the main thought bubble and the little circular parts that are always at the bottom). Your stencils are going to be more than one piece of paper, so don't worry if they are.
Once you have everything all drawn out and ironed and stuff, take one of the pieces of your stencil and put it on a towel and cut out whatever pieces are supposed to be cut out with an X-acto knife. Make sure you save the insides of the "O"s and stuff like that!
Step 4: Screen Printing
Use a paintbrush (those foam ones work best) and put paint wherever it's supposed to be.
Let it dry for a while and remove the stencil. Then repeat with the other stencil you're using.
Step 5: Cutting and Sewing
Cut out another piece of material the same size and shape as the other piece. Sew them together, wrong (wrong meaning the sides that won't be on the outside) sides together, leaving a place to put the stuffing in it.
Step 6: And Done!
Of course, you don't have to use an XKCD quote, you can use whatever kind you want.
So yeah, have fun making thought bubble pillows!