Pre-K and kindergarten-age children love puzzles, but they usually can't handle more than about 25 pieces. Wooden puzzles of the states are age-appropriate for your child, but she may have trouble focusing long enough to complete the entire puzzle.
Break the puzzle down into manageable tasks. Start with a completed puzzle, take some pieces out, scramble them and have him put them back. He wants to know how this is relevant to him, so start by teaching him states that match the letters in his name. Nathan would get Nebraska, then Alaska, etc.
Your child will find it easiest to learn the name and capital of her own state, of course. Children this age learn the things they see as useful to them. Teach her the states where friends and family live. This should get you her attention long enough to get her to learn the capitals that go with them.
Find children's books set in various states. If he connects with the story, he will be more interested in where it happened. Find interesting places to go and fun things to do in each state. Make up stories together about visiting. Copy pictures out of travel books, and paste cutouts of him and you together there. This is a good way to connect him to the capital cities.
Every state has at least one kid-friendly food you can associate with it. Make your supper menus have foods you can match up with a specific state. Let your child help you cook. Have her put the puzzle pieces for each state next to the matching food. Try to make the food associate with the state capital. You have her attention; use repetition and rhymes for the capitals. Have her put the pieces back in the puzzle after the meal.
Preschool and early elementary children love animals. Learn about the wildlife native to each state. Draw or print a picture of an animal that goes with the state, and paste it onto a large state outline. Let him color it and hang it on the wall of his room. Make sock puppets of the animal. When you make up stories about visiting a state and its capital, include the animal as a character.
Be careful---you may end up with new vacation plans.