Nutsedge requires a few years of attentive weeding to get it down to manageable proportions, and even then you'll still get stray ones coming up. I've found that it pulls out pretty easily, roots, nutlets, and all, when the ground is moist. I've even eradicated it from a patch of lawn that way. But then I love to weed. :-)

I recommend Sedgehammer, a sedgicide that has so far caused no damage to anything other than the blasted sedge in my yard.

Nut Sedges evolved in bogs, swamps, and they prefer a fairly moist soil to establish themselves, although once established they will grow in fairly dry soil. These sedges spread by tubers, rhizomes, and seeds which are dropped into the yard or garden by birds as they fly over.

Perhaps this article will be of some help.

http://ipm.ucanr.edu/PMG/PESTNOTES/pn7432.html

Nutsedge forms little bulbets in the ground, so when you pull it, the bulbets remain in the soil and grow new plants.