Graphics Card update HELP PLEASE! [=

i was wondering if someone could help me as my laptop needs to do an update for its graphics card as it is a bit old now. when i try to play on league of legends it tells me at the bottom of the screen that i need to update it but im am not sure what to do and im not to good with finding out about spec etc

here are some system details:

Inspiron 6400/E1505

Service Tag: <ADMIN NOTE:Service tag removed per privacy policy>

all i want its the most recent update of the graphics card to make it play y games thanks. [=