TheKeyMaker2 asked the following:

1. How would one go about changing or upgrading a graphics card in a laptop?
   Upgrading a laptop video card usually involves removing the base-plate of the laptop case, removing several screws and removing the video card. Be careful, the fan on the card is often connected to the laptop's motherboard.
   
   Being careful of the connectors, plug-in the new video card (and fan if needed), screw the card down and replace the base-plate.
   Before replacing a video card make sure to uninstall the previous drivers before you remove the card from your system. I recommend using Driver-Cleaner Pro ( http://www.drivercleaner.net/ ) as it does a good job and is free for personal use.
   
2. Is it possible?
   Sometimes. It all depends on the model card you currently have. If you are lucky enough to have a laptop designed for gaming and it has a removable video card, you should be able to replace it (presuming you can find an upgraded card that works with your socket type and form factor - AGP, PCI, M9, etc. ). Make sure you have a non-integrated card. Integrated cards are part of the motherboard and can't be upgraded (eg: the ATI X1100 is the integrated version of the ATI Radeon X300).
   
   If you have one of the new range of mobile cards produced by nVidia or ATI that won't be a problem. However if you have an fx Go5600 or fx Go5700 then I'm sorry to say that you are, like me, stuck with it (note: that laptop was stolen so now I have an ATI Radeon X1800XT). I discovered after the fan on my card konked-out (3 days after the warranty expired of course) that the Go5x00 series of mobile cards went out of production almost 12 months ago and all the stocks are sold (mostly to people who bought extended warranties and had the cards replaced).
   
   The following is a list of fairly common mobile video cards. Cards within a colour range can usually be interchanged with each other. The cards in the very high-end of the performance scale are usually only suitable for larger (17" screen and larger) laptops due to the power consumption and heat. Cards are listed from slowest to fastest in each section, with slowest at the top and fastest at the bottom.
   
   
   === Integrated Cards (non-upgradable) ===
   Intel GMA900*
   Intel GMA950
   ATI Radeon Xpress 200M
   Nvidia GeForce Go6100/6150
   ATI Radeon Xpress 1100/1150
   ATI Radeon Xpress 1200/1250
   Intel GMA X3100
   Nvidia GeForce 7150M
   * denotes NOT Vista Aero capable
   
   === Low-End Cards ===
   Nvidia GeForce Go6200
   Nvidia GeForce Go7200
   ATI Mobility Radeon X300
   Nvidia GeForce Go7300
   ATI Mobility Radeon X1300
   ATI Mobility Radeon X1350
   ATI Mobility Radeon X2300 
   
   === Mid-Range Cards ===
   Nvidia GeForce Go6400
   ATI Mobility Radeon X600
   Nvidia GeForce Go7400
   ATI Mobility Radeon X1400
   ATI Mobility Radeon X1450
   Nvidia GeForce 8400M-GS/Nvidia GeForce 9300M-GS
   ATI Mobility Radeon HD 2400
   
   === Performance Cards ===
   Nvidia GeForce Go6600
   ATI Mobility Radeon X700
   Nvidia GeForce 8400M-GT
   Nvidia GeForce Go7600
   ATI Mobility Radeon X1600
   ATI Mobility Radeon X1700
   ATI Mobility Radeon X2500
   Nvidia GeForce Go7700
   Nvidia GeForce 8600M-GS
   Nvidia GeForce Go7600GT
   ATI Mobility Radeon HD 2600 DDR2
   Nvidia GeForce 8600M-GT DDR2
   Nvidia GeForce 9500M-GS DDR2
   ATI Mobility Radeon HD 2600 GDDR3
   Nvidia GeForce 8600M-GT GDDR3
   ATI Mobility Radeon HD 3650
   Nvidia GeForce 8700M-GT
   Nvidia GeForce 9650M-GS
   
   === High-End cards ===
   Nvidia GeForce Go7800
   ATI Mobility Radeon X1800
   Nvidia GeForce Go7900GS
   ATI Mobility Radeon X1900
   Nvidia GeForce Go7800GTX
   ATI Mobility Radeon X1800XT
   Nvidia GeForce 8600M-GT SLI
   Nvidia GeForce Go7900GTX
   Nvidia GeForce Go7950GTX
   Nvidia GeForce 8700M-GT SLI
   Nvidia GeForce 8800M-GTS
   Nvidia GeForce Go7950GTX SLI
   Nvidia GeForce 8800M-GTX
   Nvidia GeForce 8800M-GTX SLI
   
   Here is the entire list sorted from slowest to fastest (including integrated cards):
   Intel GMA900*
   Intel GMA950
   ATI Radeon Xpress 200M
   Nvidia GeForce Go6100/6150
   ATI Radeon Xpress 1100/1150
   ATI Radeon Xpress 1200/1250
   Intel GMA X3100
   Nvidia GeForce Go6200
   ATI Mobility Radeon X300
   Nvidia GeForce Go7200
   Nvidia GeForce Go6400
   ATI Mobility Radeon X600
   Nvidia GeForce Go7300
   ATI Mobility Radeon X1300
   ATI Mobility Radeon X1350
   ATI Mobility Radeon X2300
   Nvidia GeForce Go7400
   ATI Mobility Radeon X1400
   ATI Mobility Radeon X1450
   Nvidia GeForce 8400M-GS
   ATI Mobility Radeon HD 2400
   Nvidia GeForce Go6600
   ATI Mobility Radeon X700
   Nvidia GeForce Go7600
   ATI Mobility Radeon X1600
   ATI Mobility Radeon X1700
   Nvidia GeForce 8400M-GT
   Nvidia GeForce Go7700
   Nvidia GeForce Go7600GT
   Nvidia GeForce 8600M-GS
   Nvidia GeForce Go7800
   ATI Mobility Radeon X1800
   ATI Mobility Radeon HD 2600 DDR2
   Nvidia GeForce 8600M-GT DDR2/Nvidia GeForce 9500M-GS
   ATI Mobility Radeon HD 2600 GDDR3
   Nvidia GeForce 8600M-GT GDDR3
   ATI Mobility Radeon HD 3650
   Nvidia GeForce Go7900GS
   ATI Mobility Radeon X1900
   Nvidia GeForce Go7800GTX
   ATI Mobility Radeon X1800XT
   Nvidia GeForce 8700M-GT
   Nvidia GeForce 8600M-GT SLI
   Nvidia GeForce Go7900GTX
   Nvidia GeForce Go7950GTX
   Nvidia GeForce 8700M-GT SLI
   Nvidia GeForce 8800M-GTS
   Nvidia GeForce Go7950GTX SLI
   Nvidia GeForce 8800M-GTX
   Nvidia GeForce 8800M-GTX SLI
   
   
   
3. If it is, does it cost a lot?
   The higher-end cards cost anything up to US$500 (or more) but mid-range cards and performance cards are more in the range of $200-$350, when I last checked. The price is comparable to a video card for your desk-top machine.
   
4. Could I do it myself?
   Probably, the Instructions are quite clear that come with the cards or laptop.
   BE WARNED! Replacing the video card yourself may void the warranty on your laptop or video card. When in doubt take it down to the local computer shop and they'll do it for next to nothing for you. Ask them about the warranty first.
   
5. Where would i get one?
   The same place you would buy a desktop video card. Most computer stores will order one in for you. Or if you could always just buy one online.

I hope this answers your questions sufficiently. 8)

*edit: Updated card list on 28th May 2008*

Thank you very much, that helped me out a whole bunch.

Now, to get the money...

Nicely done!

One thing I might add:  if you're going to replace the video card yourself, you can often confirm if it's compatible with your mobile hardware by looking up the form factor.  Not the kind of thing you'll see in the sales brochure, but detailed tech specs or technical forums will usually tell you what that is.  For example, my laptop was hosed because its card was a non-upgradeable form factor (I think it was called "form M9", or some such).  I'd found the next step up in mobile video, but it was the wrong form factor--therefore, I saved myself from buying the wrong fit.  Usually though, you can find someone online who's already tried/done exactly what you're trying to do, and you won't even have to go this far.

Happy belated-by-2-months 2nd birthday to this thread... update to card list in the next day or so... just compiling the info now.