How do you replace an old 2 prong plug with an updated 3 prong plug?

You don't. A 2 prong plug has two wires, one called live (black or red wire in the US) and the other is neutral (white or gray wire in the US). A 3 prong plug needs a third wire for ground (bare copper, green, or green-yellow in the US).

The only time you can replace a 2 prong plug with a 3 prong plug is if the 2 prong plug incorrectly replaced an original 3 prong plug.