Flash cards are a tried and true method in part because they work for many children. Make flash cards for all of the multiplication tables and then work on five of them each day. Pull them out at different times of the day and flip through each of the cards 10 times. Take five different cards for the next day. At the end of the week, review the 30 cards that you worked on during the week. Pull out any that you don't know easily and review them each day of the next week in addition to five new ones each day.
Rap music can work for the rhythmic learning of multiplication facts. Or you can simply take your favorite genre of music and sing your math facts every day. Turn the multiplication tables into the lyrics of your favorite tune and sing those lyrics every day until you have them memorized. Research has also shown that drum beats can help students memorize things, so speak your math facts out loud to the rhythm of a beating drum, clapping hands or bouncing ball.
Make up word tricks to help you visualize and memorize math facts. These can take the form of stories or rhymes. For example, to memorize 8 x 8 = 64, you can say, "I ate (8) and I ate (8) until I was sick (6) on the floor (4)." Create rhyming couplets such as "Chicks, Chicks, Dirty Chicks, Six times six is 36." Make stories with words such as "To drive a 4x4, you must be 16 years old."
Some math facts become easy once you learn some number tricks. For example, 10 times any number is that number with a zero at the end. The associative property of multiplication means that 3 x 6 is the same as 6 x 3. Once you've learned one, you've learned the other. To learn the nines, hold your hands out in front of you with your thumbs touching. Counting from the left, curl the finger down that represents the number you are multiplying by nine. The numbers to the left of that finger make the first digit and the numbers to the right make the second digit. So if you are multiplying 9 by 5, you would curl your left thumb down leaving four fingers to the left and five to the right: 45.