Overdyeing is basically dyeing something that's already been dyed. It might be a fabric that you've already hand dyed, or it might be a commercial fabric (including clothing.) Overdyeing commercial fabric can be a great way to improve an ugly, or to get several fabrics to have a common tone. Remember that the dyes we're using only work on natural fibers -- if your fabric has polyester, those fibers won't take the dye.
As always, I'll assume you are familiar with preparing fabric for dyeing, the basic ingredients, and how to do the one-color baggie method of dyeing. If it's been a while, take a moment to review these.
First, I'll need to spend just a minute talking the pigments in the dye we're using. This is important for successful overdyeing, so please don't skip this paragraph. Procion MX Fiber Reactive Dye (the stuff we use) is a transparent pigment. What that means is that when you add a second color, you still see the first color through it -- it's like adding a layer of cellophane, rather than adding a coat of paint. So if you have a piece of fabric you've dyed blue, and overdye it yellow, you will end up with green, not yellow. (Of course, any areas on the original fabric that were still white will end up yellow.) And since dye is additive, you can't end up with a lighter color than you started with by overdyeing. (In other words, there's no such thing as white dye.) If you're trying for a specific color combination, you may want to have an artist's color wheel on hand. You can find this for sale at any art supply store or good paint store, and your local public library will have books on color theory that show what you get when you mix different colors. But also feel free to experiment randomly -- that's how I learn the most, and you probably will too.
If you are overdyeing a piece you've previously hand dyed, make sure the fabric is clean and damp, and then use your favorite method of dyeing -- baggie, cup or vat. The fabric won't take the second dye quite as intensely as the first dye, so overdying a blue fabric with yellow won't be exactly the same as overdying a yellow fabric with blue. Rinse and wash as usual.
Now for commercial fabrics. Again, bear with me for a short technical explanation. You have two obstacles when it comes to dyeing commercial fabric. One is that the fibers are probably already saturated with dye, and there's very little room for more dye molecules to attach. (That's true even for light colors.) So you'll need to experiment, and perhaps mix your dye a little stonger than usual. But, you say, I'm dyeing a fabric with lots of white! Well, that leads to the other problem. Most white fabrics have "optical whiteners" which make the fabric look brighter and whiter. Although they aren't dyes, the optical whiteners take up the space where dye molecules want to be, and again the fabric won't dye as intensely as a PFD will.
Okay, I lied. There's a third obstacle to dyeing commercial fabrics. (But I look at it as a design element, so I never count it as an obstacle.) More and more commercial fabrics are incorporating paints. This is really common with metallics and white-on-white fabrics. The paint acts as a resist, and keeps that area from accepting the dye. So if you use blue to overdye a white-on-white that has little white stars, you could end up with white stars on a blue background. Personally, I think it's really cool, and these have been a big hit with my quilty friends.
Now that I've given you all the problems with overdyeing commercial fabrics, you're going to find out that it's actually quite easy to do. First, do an especially good job of preparing your fabric. Then dye by your favorite method (baggie, cup, or vat). I will usually let commercial fabrics sit in the dye for 24 hours to get the maximum amount of dye to adhere. Then rinse and wash as usual.