This video shows you the easiest way I know to teach kindergarteners and above about odd and even numbers. The method is based on the concept of pairs of friends. The concept of even and odd should be taught when the child understands pairs and cardinality i.e., quantification rather than just learning a rote number sequence.
Of course, later, when the child reaches an appropriate age, the child can simply remember this concept - If the units digit (or digit in the ones place) is 1,3, 5, 7, or 9, then the number is called an odd number, and if the units digit is 0, 2, 4, 6, or 8, then the number is called an even number.
