Introduce your kindergartner to real American coins or bills. Give her a variety of denominations to play with and instruct her on how much each coin or bill is worth. Have her sort the coins or bills into denominations and order them from lowest value to highest.
Quiz your kindergartner by asking him to give you specific amounts of money using one denomination. Ask for fifty cents using only quarters, then for the same amount using only dimes and only nickels.
Help your kindergartner come up with specific amounts of money using different denominations. Practice over and over again until he is comfortable mixing and matching coins and bills to produce a certain value.
Set up a toy shop in the classroom or at home. Attach price tags to items. Give your kindergartner some money and allow her to "buy" one item using exact change. Help her out if she struggles to find the correct amount.
Integrate money counting into daily life at home or in school. Have your kindergartner "buy" an item each day, such as a book to read to a toy to play with. Increase the complexity of the price tags as your kindergartner becomes more comfortable with counting money.