Is it possible to upgrade a laptop's graphics card?

Normally NOPE, unless it is a VERY high end system, Like Alianware.

Sometimes, if the card is on a mini-PCI slot. Usually you can take the little covers off on the bottom of the case, and if you see anything label with the typical video card brands, you can replace it.

Pretty much the only other way is to replace the motherboard.

On a side note, if the laptop uses shared video memory, sometimes you can set the BIOS to use a little more RAM and it will increase the video performance.