What I have my 8th grade students do, as far as memorizing is concerned, is make flash cards with the first 20 elements, from hydrogen to calcium. On these flash cards they have the element name on one side of the card (correctly spelled), while on the other side of the card, at the top we have the atomic number. In the middle of the card, we put the atomic symbol, using the correct rules of capitalization. At the bottom, we put the rounded atomic mass number. I have them drill with the flash cards for about a week, then we have a "fill-in-the-blank" type test to assess their knowledge.
As far as navigating the periodic table, I stress to my students the different groupings across the top of the chart, starting with group 1, the alkaline metals. Then, group 2, the alkaline-earth metals, skipping over to group 7A (or group 17, depending on your textbook), the halogens, finishing with group 8A (18), the noble gases. We come back and visit the transition metals, which serve as the bridge, later.
I dissect the chart by color, showing students that most of the elements are metals, on the left of the chart. To the far right, we have nonmetals. The stair-step line, which serves as the border between those two groups, are flanked with metalloid elements. The periodic table is like everything else, of studious substance: the more you work with it, the more familiar it gets.
Its just like Multiplication table you have to keep on reading and repeating it.
The best way to remember is, read in the streach of 10 elements and try to remember it and when you are done with it move to next 10 elements then again read it from the starting and remember complete 20 elements. and when you are completely confident that you remembered the first 20 elements then only move to next 10 and then next 10 and follow the same procedure.
The ultimate way to remember will be read it in a rhyming form and follow same process as i mentioned. And your task of remembring becomes simple.
Do it every day.
To make it easier to memorize the elements in the periodic table, you have to make flashcards. Flashcards help with a lot of things and using them makes it an easy way to learn. Write the the chemicals or elements with the abbreviations on the front and on the back write down what number that element is.
Memorizing the period trends (ionization energy, size, etc) helped with navigating the table. Breaking the table up into its components (noble gases, transition metals, metaloids, non metals, etc) also helped with memorization since you could go at it bit by bit.
Flashcards are your friend. You can even have yours color coded to match its categorization.
I made flashcards with the atomic mass and number behind, also a catchy song can help, just make up a beat and have fun making lyrics.