The way the brain works is that you learn from repetition, the more you do something the better you get at it. So the more you review the first 20 elements on the periodic table, the more often you'll be able to remember it until you're about to recount them without hardly thinking of it.
My advice to you is to grab some pieces of paper. Cut them up into sixths until you have twenty of them, then write down on each smaller piece of paper the numbers 1 up to 20. Then on the other side of the paper, write down the element. Do this in accordance to their position on the periodic table. Then spend some time guessing as to what element is on the other side of the numbered paper. You'll start guessing, "the first element is Hydrogen. The second element is Helium." And so on. Rinse and repeat until you're able to guess the element depending on its placement on the periodic table. Good luck!
