The next day, drain out this soaking water from the pot, and rinse the chickpeas once or twice in cold water. Do this by filling up the pot halfway, stirring the chickpeas around and then pouring out the excess water.
Add 3 cups of fresh cold water to the pot and then place the pot uncovered on the stovetop on a medium heat setting. Once the pot contents start to boil gently, place the lid on the pot (leaving a small opening slit) and let the pot contents continue to simmer for 30-40 minutes. Adjust the stove heat setting as needed to keep the pot contents bubbling gently.
When cooked through, use a slotted spoon to remove the cooked chickpeas into a separate bowl to cool.
If you prefer to use the slow cooker, you can cook the soaked chickpeas in a slow cooker for 3-5 hours on a low setting, along with half an onion and enough liquid to cover the chickpeas by 2-3 inches. Reserve the yellow colored chickpea cooking liquid as this makes a great vegetable broth base for other dishes (this keeps in the fridge for a few days).
Any leftover cooked chickpeas can be stored in the refrigerator for a few days, to be used in different recipes. Often recipes with long cooking times will likely call for using uncooked (but soaked overnight) chickpeas, so be sure to check the recipe before cooking them.
Cooked chickpeas also freeze well in the freezer so you can make extra and just freeze a portion to take out later and thaw to use in another dish.