They always say that a child mind is like a sponge. It absorbs everything they hear, see and learn. I wanted to share my experienced as a mom how Gabz developed her memorization skills.
We used to borrow books from the library almost every month. There is one particular book that Gabz loves to read (or rather memorized). She is three and does not know how to read yet, but since she loves books, I always read to her any books we could grab. There is one book "Where is the Green Sheep?" which I read to her in the car while waiting for her Dad. I was surprised when we arrived home she started to read the book by herself, exactly the way I read it. She loves the book, that is why it was so easy for her to remember everything.
Another thing is repetition or constant practice. When we were teaching her how to answer questions like, What is your name? How old are you? and How are you today?, we asked her these questions many times a day. Sometimes she got mixed up that when you asked her, how are you today?, she would answer you "I'm three years old!" LOL But eventually, asking her many times a day, she was able to answer these common questions properly.
Make things fun or incorporate things in a game. We do this with Gabz when we teach her how to do addition. For me it is quite early to teach her, but she has a book that has simple addition and subtraction on it, and she would always asked me to teach her. So every time we are in the car, we always plays addition game to pass the time.
I think, the most important thing for them to be able to memorized things, is to make them get excited or interested. Once you have their attention, it becomes easier and fun.