What is your backpack made of? You must match the type of dye you use to the fiber it's made out of. Cotton is not the only fiber that can be dyed, but other fibers require different dyes to dye well.

Most Jansport backpacks are made of nylon, which can be dyed with acid dyes, if you heat them in the dye with an acid in a large enough pot on top of the stove. You can't dye nylon at room temperature. (Note that you should never again use this pot for cooking, because all fabric dyes may contaminate food.) If your backpack is made of polyester, you can't use acid dyes; in that case, you must use disperse dyes. See How to dye nylon and How to dye polyester for instructions and more information.

Is your backpack water-resistant? Oftentimes a waterproof coating is sprayed onto backpacks. If water beads up when you splash it on the backpack, instead of soaking in immediately, then you won't be able to dye it. A backpack that repels water will also repel every sort of dye.

What color is your backpack? Dye is transparent, so it will not show on top of a dark color. Whatever colors are already on the backpack will still be there after you dye. This means that in many cases the only practical color choice is to dye it black. The only preexisting color you can dye in different bright colors is white.

As an alternative to dyeing, you can use a nice soft fabric paint, such as Dharma Pigment Dyes or Jacquard Dye-na-Flow. Unlike dye, fabric paints do not have to be boiled into the fabric, so they can be applied at room temperature. However, they will work only on uncoated fabric, not on coated nylon. After drying, Jacquard fabric paints require heatsetting in a commercial dryer (home dryers won't get hot enough) or else the addition of an acrylic catalyst such as Jacquard AirFix to the paint before you use it. Any surface treatment of your backpack's fabric will prevent anything you use to change its color from working. If it's water-resistant, just forget the whole project.

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[Portions of this answer were originally posted, by me, on September 5, 2008, on Yahoo Answers.]