I think the explanation is fairly simple. Grab two of the same item, I'm gonna use apples for this example.

First, hold one apple in each hand. Ask your child how many apples you have in one hand, them the other hand, then the total.

Then, hold two apples in one hand, with the other hand empty. Point out that you have two in one hand, and none, therefore zero, in the other. Have your child count the total number of apples, 2, and explain further how zero stands for no quantity. How when you have zero of something, you really have none.