Most laptops have the GPU soldered onto the motherboard, which means you need specialist tools/experience to replace. Some laptops on the other hand use a standard socket which offers limited upgradability (e.g. the customisation offers on Dell laptops). In most cases, you should look for the technical specifications for your laptop to find out what upgrades it supports, if any at all. To my knowledge, there are very few laptops at all that use "graphics cards" - only the GPU with specialized cooling specifically for the laptop/motherboard (which also means that upgrade options are limited due to the fact that you generally can't upgrade the cooling).
Tip: Opening up the laptop is the first step - look at the motherboard, locate the GPU, and try to identify how it's attached (i.e. hard solder, or socket).
On the other hand, finding a place to buy GPUs can be quite difficult, and it's almost always very expensive.
Finally, your case specifically - a quick google tells me your laptop has a Mobility Radeon HD2300, which is an IGP, and almost certainly hard-soldered to the motherboard. It's also a budget IGP (i.e. lowest of the range), so it's unlikely that your laptop can handle any better GPUs. Your best bet is a newer laptop, or a desktop (unless you really need the mobility of a laptop), or as above - updated drivers.