In years past I simply allowed the sunflower plants to bloom, wither, and die, after which I chopped down the stalks for compost. However, this year the plants seem to be productive much longer, and the pruning of dead flower heads and withered leaves seems to force the plants to continue the mechanism by which flower buds appear.
The flowers that appear after the deadheading process commences tend to be smaller and a sometimes bit on the spindly side, but I suppose this is the price one pays for screwing around with natural plant rhythms. I also would not recommend sunflower deadheading if you plan to collect seeds, or if you plant sunflowers to feed the local wildlife. However, if sunflower blooms are what drives you to plant the seeds in the first place, consider aggressively pruning your sunflowers to stimulate more blossoms.