Getting a good night sleep with a new kitten in the house can be difficult. The biggest thing that can help is to maintain a routine for sleep, play and eating. Make sure your kitty gets plenty of exercise and frequently opportunities to eliminate.
Play time should be at least 2 hours before the designated "sleep" time. Ensure you have plenty of toys and know the types of games your cat likes best. Play for at least 30 minutes each day.
For more information please read Selecting the Right Toys for your Cats Play Preference