After 24 hours. Do brush your teeth gently. Avoid brushing around the extraction. And don't use any toothpaste at all. Rinsing toothpaste from your mouth may dislodge the blood clot.
Follow Instructions. Your oral surgeon should have given you post op instructions... they all do. It is critical not to disturb the clot or the sutures by either brushing or rinsing. After 24 hours gentle brushing and rinsing should be fine, but you should confirm this with your surgeon for your situation since every extraction is different.