One way to teach children the times tables is by teaching them various systems of counting. If children can learn to count by ones, twos, fives and 10s, they have already learned the times tables for those numbers and are ready for harder ones.
Another method for teaching children their times tables is to teach them the concept of gridding. For instance, the multiplication problem three times three can be represented by drawing a grid that is three squares across and three squares tall, like a Tic-Tac-Toe grid, having nine squares in total. Adding in an additional row to the grid turns it into a three by four grid, which has 12 squares.
A third method useful for teaching children their times tables is chunking. Chunking allows them to break down the problem into more manageable parts and is also very useful for working with money. A problem might be how to divide $73 into individual notes. The most efficient way would be to use three $20 bills, a $10 bill and three $1 bills. Mentally, the child can break each part into chunks: 73 divided by 20 is 3 with a remainder of 13. Then, 13 divided by 10 is 1, with a remainder of 3. Finally, 3 divided by 1 is 3, giving the answer.