There are lots of ways to memorize things like the multiplication tables. Which one will work best depends on you. Think about how you learn other things best, and what you like best. People learn in different ways. Make a copy of this multiplication table.
Some people get so they can visualize the table in their heads.
Play it over and over, while you're washing dishes or whatever. Maybe writing it out over and over will help. You could even get artistic. Maybe doing numbers in different colors or odd shapes will make them stick in your mind. You need to do lots of real problems.