The symbols for the elements are associated with words that form a phrase. If you can remember the phrase and know the symbols for the elements then you can memorize the order of the elements.
Hi! - H
He - He
Lies - Li
Because - Be
Boys - B
Can - C
Not - N
Operate - O
Fireplaces - F
New - Ne
Nation - Na
Might - Mg
Also - Al
Sign - Si
Peace - P
Security - S
Clause - Cl
A - Ar
King - K
Can - Ca
Hope it helps