Kids have an intrinsic feel for the beat of most music.
To start off the very little ones, ages 18 months to 3 years, hand out percussion instruments such as wood blocks, maracas, drums, jingle bells, tambourines, etc. Show them the beat by playing a 4/4 bar: 1, 2, 3, 4, 1, 2, 3, 4.
Sing a familiar song such as “The Ants Go Marching,” “The Grand Old Duke of York,” or “Itsy Bitsy Spider,” playing the beat on a drum to show them how it should sound. They will learn visually as well by watching you play.
After they can play a steady beat they may enjoy marching to a couple of these songs. Their hands and feet go together, 1, 2, 3, 4, as body movement is an extra aid to the memory process.
Check out my sample of “Six Little Ducks” which is also a great one for keeping a steady beat.