Though simple multiplication tables may be committed to memory, it is important to understand mathematical multiplication on a conceptual level in order to multiply larger numbers. When two numbers are multiplied, the first number is added to itself the number of times specified by the second number, or vice versa. Understanding this abstract operation allows you to multiply any numbers together, and also makes simple multiplication much easier.
Visual representations of multiplication help you learn multiplication by associating the abstract mathematical concept with the visual part of the brain, which is separate from the mathematical part. Visualization is also helpful in memorizing basic math functions. Multiplication tables help to quickly visualize the products of any two numbers. Another visual method is to write out multiplication functions on the face side of flash cards, and write the product of the multiplication on the backside. Flip through the cards, turning over each side, to help yourself visually commit the numerical products to the correct multiplication function.
Just like visual representation, musical association help you memorize basic multiplication functions. Associate a song with the chronological products of a string of numbers. Then, when it comes time to recall the multiplication products, sing the song in your head to easily recall the correct products. A good association to remember multiplication rules is to create an acronym or acrostic for the operation functions. A popular example of this is the sentence "Please excuse my dear Aunt Sally," which is an acrostic for the mathematical order of operations, namely "parentheses, exponents, multiplication, division, addition, subtraction."
The most important method for efficiently learning multiplication is repetition. This includes the various multiplication memorization techniques, as well as learning to efficiently work through multiplication problems. By repetitively practicing multiplication problems, the concept becomes much easier for your brain to carry out. This allows you to efficiently complete multiplication operations in your head, which is necessary both for quickly solving simple multiplications as well as for breaking down larger numbers to multiply them on paper.