You cannot switch graphics cards as both of you are not using graphics cards, but instead video integrated with the motherboard.
From your Specs, it sounds like you have a Dell Dimension 1100/B110 model. Unfortunately, these are budget/disposable computers and not very upgrade-friendly. They do what they are designed to do well- which is surf the net, email and basic windows applications. They are very ill-suited for gaming though.
If it is indeed a B110, then it only has PCI-slots, very poor cooling, and very marginal power supply (250W peak, but more often only about ~200W sustained output). While it is indeed possible to upgrade your gaming capabilities, you have to ask yourself if you wish to invest in this system when funds would better saved towards a budget/new system with many more capabilities and upgrade possibilities.
If you're hard set on upgrading, your best route would be to start with a PCI 3d card as the 1100/b110 do not have agp nor pci-express slots for adding a "real" 3d gaming card. Luckily, VisionTek makes an X1300 Radeon in PCI and this is your best option.
The next order of business is- are you interested in buying a 3d card to help with games.. and if so, what region of the world are you in? Guidance finding a vendor/place for purchase as well as pricing will need geographic location as we have users from all over the world here.
EDIT- if you're in the USA, this jobber is what I'd recommend, provided your power supply is in good order and isn't weakened/old:
http://www.newegg.com/Product/Product.asp?Item=N82E16814129062