You aren't really "supposed" to dye eyebrows, but we do in the salon all the time, and master make-up artist Kevyn Aucoin does it as well. Go to a salon for the best results, but here's some tips. (I think Sally's may even sale an eyebrow color kit).
Just mix a bit of color just a shade or two lighter than your natural brows, you don't want your brows to be the same color as your highlights (it'll look weird), even most natural blondes have darker eyebrows.
Put a bit of vaseline around the skin surrounding your eyebrow hair. Take a dry mascara wand (for thicker brows) or a q-tip and brush a small amount of color on at a time. Be sure you brush the hairs up and then down to get all the sides of the hair, so you won't be left with splotchy parts.
Depending on the color directions, you only need to leave the color on for a short time, maybe 5-10 minutes or so. Then, take a warm, wet, soapy washcloth and wipe the color off.
Of course, be careful not to let the color get in your eyes (it can cause serious reactions, as well as blindness), most creame colors don't drip anyways, if your color is drippy at all, then don't even attempt it.
Also, if you have very sensitive skin, mixing a packet of Sweet 'n Low in the color will help numb the skin so it won't sting as much.
Keyvin Aucoin suggests in his book "Making Faces" to use facial hair bleach on the brows. Just be sure you scrape off some of the creme to check the color every few moments, and then cover the spot again to check the color (b/c you don't want to end up with orange brows). You don't want to leave it on for too long, b/c it could cause some of the hair to break off.
When the color is ready (shouldn't take long, just watch it), wipe it off with the wet, soapy cloth, follow with a mild anteseptic and a bit of hair conditioner to keep the brow hairs supple again.