I am also an elementary teacher and agree with Lisa. Make sure addition and subtraction are down pat (if the child is in 1st or 2nd grade or younger). Skip counting by 2's, 3's, 4's, 5's, and 10's really help.
Also, a CHEAP manipulative is red kidney beans or pasta. Have your child group them into piles and talk about what 2 X 3 means. I also use words and examples that children can relate to. There are two kids and mom wants to give each kid 3 cookies each. How many cookies does mom need to buy? I then follow it up with a "joke" of "those kids must have been really good, eh?"
The more you relate it to their world, the easier it will be for them. Some kids are natural drawers, so have them draw sets of items. For one student, I made separate manipulatives for each set of numbers. One's was a dog and I printed off a bunch of bones. Two's were cats with milk bowls. It made her able to remember the numbers with the animals and make it make more sense to her. Not all kids need this, but this is just an example of how to tailor what you are doing to the child's learning style.
Good luck and have fun. Also, keep the chart away as long as possible. Usually, I don't pull it out until I teach division and use it for the kids that didn't learn all of their facts but need to learn the steps to division. In the classroom, you sometimes have to push the kids along even when they haven't totally mastered the steps before it (esp. with math facts). As a parent, you don't need to push the child ahead if they aren't ready.
KEEP IT FUN! :)