To countersink holes you use a special bit called a countersink. It is used by plunging into the hole. These come in ''0'' flute, 1 flute, and multi-flute. The ''0'' flute and 1 flute tools are less prone to chatter. Normally used at 1/2 or less of drilling speed and work best with cutting oil. Commonly available in 90, 82, and 60 degree. Metric countersunk fasteners have 90 degree tapers, English screws normally are 82 degrees. I personally like M.A.Ford brand countersinks, they seem to work better than others at least for me.
https://www.mcmaster.com/#countersinks/=18wqoka
https://www.mcmaster.com/#countersinks/=18wqofo