fried chicken - how long to fry each piece?
The short answer to your question is, "until it's done".
The USDA tells us that chicken is done at a minimum internal temperature of 165 °F, so the length of time necessary to bring each piece to that temperature will vary (a thigh will reach that temperature faster than a breast) depending on its density compared to surface area.
It's sometimes easier to brown the chicken pieces nicely, then add a bit of liquid to the pan and cover it to establish a braising condition to cook it thoroughly.
Browing chicken slowly will allow the heat to penetrate deeper during the browing phase than if you use high heat. High heat will tend to brown the outside of the meat quickly while leaving the interior less done. If you want a crispy chicken and don't want to use liquid to finish it, more cooking oil at a slightly higher temperature than you'd use for braising will work better. For truly crispy chicken, the deep frying method (not necessarily total emersion deep frying) does the best job.
Breast & thighs take longer to cook as is obviously the largest pieces...typically it takes 20 minutes..you want to make sure the juices run clear, if unsure, use a thermometer to make sure its at least 165F. Legs & wings take less time, about 10-12 minutes...I usually make sure my oil is at 350-360F, which is standard. You don't want your oil higher or will scorch the breading & chicken will be raw inside nor do you want it cooler as the chicken will steam instead of crisp.
Cast iron is a good vessel to cook in however, if you don't have that, you can get great results in another type of pan or a deep fryer...