Summarize:

Cover it with water. Place the lid on the pot right when you turn it down. This is often referred to as the traditional method of cooking corned beef. After a few hours of cooking, tip 1 side of the lid up to check that the water is still covering the brisket.  Add 1 cup (237ml) of boiled water to the top of the pot, if the water is getting low. Check the meat 1 to 2 times to ensure you keep water levels high. This will replace water that is lost through steam. Every time you remove the lid, you will extend the cooking time slightly.  Test the meat with a fork. If it is fork-tender it is most likely done. Insert a meat thermometer into the center of the brisket. If the thermometer reads 145 degrees Fahrenheit (63 degrees Celsius), it is cooked.
Place the brisket inside a large pot on the stovetop. Bring the water to a boil, then turn it down to medium-low or low heat to allow it to simmer. Set your timer to boil the meat for 1 hour per lb (0.5kg) of brisket. Keep a kettle of boiled water nearby. Avoid checking the corned beef too often. Do not add vegetables until the last 30 minutes of cooking. Remove the lid when the timer beeps. Drain the meat and vegetables.