If you bring milk home from the store and open it on the sell-by date, it may be good for anywhere from two to five more days. That assumes you close the container in between uses, don't let it sit out at room temperature, and store it in the colder part of your refrigerator. It is, of course, better to buy milk a few days before that "sell-by" date.
Milk is very good at letting us know when it has started to spoil: it gets a sour smell and flavor early in the spoilage process. (Years ago, while writing a story about milk for Cooking Light, a researcher told me this: "spoiled" milk may make you sick because it is disgusting, but it is unlikely to make you sick due to pathogens.)
Milk keeps best in the cold–and dark. Buy milk in opaque containers (not glass) and keep it in the back of the refrigerator, not on the door, for maximum shelf life.
There's no need to let your milk go bad. See 7 Ways with Milk.