The seeds in the center of a sunflower need to reach maturity before they are harvested. They don't all mature at the same time, but at least two-thirds should be mature at harvest time. Seeds are mature when they are swollen, the shells are hard and they have black and white stripes.
The back of the flower will begin to turn dark brown and wither when the sunflowers are ready to be harvested. It will also be dry and the entire head will start to droop. When the back of the flower looks dry and dying, it means that the majority of seeds have matured and the entire head is ready to be picked.
As sunflower seeds mature and harvest time is near, the flower petals that were once brightly colored will begin to fade and turn brown. They will also shrivel and dry up, eventually falling off the head entirely. Once the petals are dried up, it's a good indicator that the seeds are ready to be harvested.
Birds always seem to know when sunflower seeds are ready to harvest and will begin eating them as soon as they mature. If birds are beginning to help themselves to the seeds, it's time to harvest. If the majority of seeds aren't mature, however, and the birds are just getting an early start, cover the head with a paper bag and give the seeds a few more days to mature.