Take your time. You don’t need to sit down and learn all of the multiplication facts at one time. In fact, this would be the worst way to learn. Choose a table and focus solely on that one. Take as much time as you need to master each one before moving onto the next one. Spend about 15-20 minutes each day studying flashcards or playing math games to master each multiplication fact. There are many multiplication math games with different themes that can be found online. For instance, if you really like dinosaurs, find one that uses dinosaurs to make learning more fun.
Another variation is to ask the child to draw. First make some sticks, circles, squares, or other shapes on a page, and encircle them. Make for the child a big "bubble" to draw in, and ask the child to draw either the same amount, one more, or one less. Also have your child practice writing numbers on paper.