While clowning is surely an art form, there are things you can do with children in order to get them to come out of their shell and have fun acting like a clown. The children can try several different activities that will keep them on their feet and hopefully get them interested in the world of clowning.
Monster Under the Table
One child gets under a table while the other one gets on top of it. The table must be sturdy enough to stand on. You can have the child sit instead if you feel uncomfortable with the standing. Have the child under the table attempt to touch the child on the table while the child on the table tries her hardest not to be touched. Have the children experiment with noise during this exercise as well.
Walks
A classic clowning exercise, have one child adopt a walk (it should be very distinct such as sad, prissy or giant steps). The other child will walk behind the first child and imitate the walk, but with grandiose gestures. The first child will stop to look behind them often and when they do so the other child mimicking them will try and look innocent.
Tug of War
Have two children face one another and hold an imaginary rope in between them (or you can use a real rope). Have both children pull the rope as hard as they can, but ask them to experiment with doing it in character. Have one child be a strong clown and one a flighty clown and then have them reverse. What happens when one clown loses? Does he cry? Does he laugh? Does he storm off? Have them answer the questions for their clown.