Recently we had a post about muteing colors. Now I'd like to know how do you brighten colors? I see pieces that are much brighter than the color of the polymer clay I buy.

What brand are you using?  My first instinct is that it would be hard to "brigthen" a color if that means increasing it's saturation/pureness.  It's easy to add color, but not to take it away.  I know Kato has a line of extra-concentrated colors for mixing which might result in more intense color... hopefully one of our resident gurus will have some thoughts!

There are some brands of clay that have, or had, bright neon-like colors.  I think Sculpey still has some.  That said - it's not the best brand for jewelry because it is more brittle and subject to breakage.

So, your charge is to fool the eye.  Use white as a contrast next to the color that you want to pop and it will seem brighter and more intense.  Subdue the accents and supporting colors by mixing with ecru, for example, and the focus color will have more pop and seem brighter.

When you see something that seems to be very bright, study what's around it and you will get some ideas on how to manipulate the clay to use contrast to get the desired effect.