The short version: Start with coin names, then counting by 1s with pennies, then 5s and 10s with nickels and dimes. Five minutes of real-coin play beats twenty minutes of worksheets, because kids learn money by touching it. The five games below build from "what's a quarter" to counting mixed coins.
Dump a handful of change on the table. Call out a coin ("find the dime!") and let your child pick it up. Flip it: they pick a coin and you name it. Most kindergarteners need a week of this before counting makes sense, and that's normal. If they can name all four coins without hesitating, they're ready for game two.
Line up ten pennies. Count them together, touching each one: "1 cent, 2 cents, 3 cents..." Then scramble the line and count again. This teaches the two things kids actually struggle with: that each coin is worth 1 cent, and that the count doesn't change when the coins move. Do it until it's boring, then move on.
Once pennies are easy, introduce nickels (count by 5s) and dimes (count by 10s). Line up five nickels and count: 5, 10, 15, 20, 25. Kids who can skip count already have a head start; kids who can't will pick it up fast because the coins give the numbers something to hold onto.
Set out toys with price tags under 30 cents. Your child is the shopkeeper and has to count out the right coins from a pile. Start with exact-coin prices (a 7-cent toy = 7 pennies), then allow any combination. This is the game that turns counting into actual money skill, because now the number means something.
Put two small piles of coins on the table. Ask which pile is worth more, not which pile is bigger. This one trips up almost every kid at first, because five pennies look like more than one dime. It's the single most useful money lesson in early elementary, and it's worth playing weekly until it's automatic.
These games all have digital versions in Bright Minds Club: Piggy Bank Coin Counting and Coin Sorter for the early steps, Which Is Worth More? for the comparison game, and Grocery Store Money for the shopkeeper stage. Same skills, zero setup, and the stars they earn carry over to their cat's wardrobe.