Memorizing the periodic table
There isn't really much sense in memorizing the periodic table. The elements you often use you will know them by heart after a while. And you can always use a table when you need it for the others.

That being said if you really want to do it, mnemonics are probably the best solution to memorizing the whole table. You can find some here :

https://www.mnemonic-device.com/chemistry/periodic-table/mnemonic-device-for-the-periodic-table/

or here :

http://en.wikipedia.org/wiki/List_of_chemistry_mnemonics#Periodic_table