Making flashcards is perhaps the easiest way to remember the periodic table. Small note cards that have the symbols of each element on one side and the names on the back can be arranged to make a large scale model of the table to work off of. Color code based on metals, metalloids, halogens etc.
Completing practice worksheets is another way to memorize and guarantee you know what you are learning when it comes to this type of subject matter. Make worksheets of two types. One can have the full English written out names of chemical elements with a blank line next to it for the symbol. A second kind can have symbols with space left for the full name. This reversal process will help in getting the knowledge back and forth.
Work on chemistry problems. Application is key when it comes to any memorization. By using the chemical element names and symbols interchangeably throughout the student's chemistry homework, they can gain a better handle on how each element behaves and subsequently add personality to it. This will help them remember the individual elements as distinct rather than one of many.