You don't, in theory, because the ground wire is missing. But if you must, cut the end of and add the new three pin plug, the two flat pins are for the two wires, the round is for the ground that is...
The third pin usually on the bottom is the pin that goes to the ground/earth. <<>> See Sources and Links below.
It really depends on what type you plug you are using. From your use of...
The earth, or ground, pin on a 3 pin plug is a connection to safety ground. It is intended to be connected to the chassis of the appliance, in such a way that operational current never flows on that...