I memorized my time tables through playing online math games when I was young.

Flashcards also helped tremendously.

You could also memorize the time tables through 5, and when you get a bigger number, multiply it by two.

For example, if you have 8x7, go to 4x7 and then double it. I'm not actually sure if this method makes it easier or harder to come up with the number, but I used this method if I ever forgot a number.