Sing songs with hand movements. There are multiplication albums that sing the times tables. You can listen along and learn the times tables through music instead of rote memorization. Listen to a few different versions and find one that works best for you. Add in hand motions or dance moves that illustrate the different number pairs to make the process more interactive.
Learn one table at a time. Select one multiplication table to learn at a time. Start with the simple tables such as 2s, 10s, 5s, and 11s. By the time you learn the more difficult tables such as the 7s and 8s, you will already know several facts. Remember, 1 x 4 is the same as 4 x 1 so you only have to learn half of the multiplication table because the other half is just written the other way.