I'm not aware of a site like the Crucial Memory Advisor (brilliant tool, I agree) which can scan the PC and give information about possible graphics card upgrades. There may be one, but it can't be well publicised as I have yet to come across it.
The problem comes when the graphics chip is a built-in one onboard the motherboard, since it is unlikely a tool is going to be able to differentiate between an in-built one and a card in an expansion port. It may be able to, but I doubt it.
I would still tell the customers to open their case and take a look inside. So, my process in simple bullet points would be:
*Look inside your computer. Where the cable from your monitor connects back to the rear of the chassis, examine this connection. Is it mounted and soldered directly to the motherboard (like the Mouse/Keyboard ports) or is the connection back to a separate card, which is mounted at 90° to the large motherboard inside the computer?
If the former, then your graphics chip appears to be built into the motherboard itself and you are going to need to ensure that you purchase a graphics card with a dual-monitor output.
If the latter, then you can proceed to the next step
*Now show the client a picture of a PCI-E port, then a PCI port and then an AGP port. Ask them for each one if they have something which resembles one of these ports on their main board which doesn't have anything connected to it. If they do, they can stop there as they have now determined what type of card to buy. You want them to look for a free PCI-E port first, then a PCI port and finally an AGP port - although it is unlikely they will have one of these if the graphics is onboard, or if they do, it will be filled with an existing graphics card.
Of course, don't forget to include steps regarding what to do if they don't have any ports left but an AGP port inside their PC (for clients with older PCs). In this case, they are going to need to take out the existing AGP card and replace it with a dual-output AGP port.
I hope this helps,
-Matt