Im planning on buying a D-Link 802.11G Wireless Base Station and i want it to connect two of my computers, i have a cable modem. Do i need to buy like a card and install it into the back of the computer for my computers to pick up the internet connection off the router ?

Yes ,you need a Wireless Ethernet adapter card for each Computer .I recommend buying one from Dlink since they are designed and obviously tested by the same company,but it is not absolutely necessary.The most imoportant thing ,is that the adapter uses the "G" level bandwidth. Check the owner's manual for the router surely they recommend a model .These cards are mounted inside the computer case.
BTW if one of these computers is a Laptop check to make sure it doesn't already have a wireless adapter .They are quite common now.

I'd not recommend you use an internal wireless adapter unless it is a laptop. Laptops usually have the antenna routed either around the bottom plastics or around the LCD, but desktop systems using internal cards rely on a small POS antenna that sticks out the back and if your case is stored inside a desk or close to a wall, this causes interference problems in many cases. The USB adapters are best for desktops IMPO, and PCMCIA adapters work best for laptops, though systems that route the antenna around the LCD are almost as good with a mini-pci.
I'd also not recommend D-Link, their support is crap, their units are junk and they have compatibility issues, especially with their + series which is not fully compliant. I'd recommend Linksys or Orinoco, but whatever you buy, do try to get the same manufacturer cards, Liquidlen is correct about that part, using same manufacturer hardware will ensure the best results, especially if you plan to use range entending or speed boosting tech(these things are usually not universal standards)

A few other tips, don't locate your router in a closet, that's asking for interference problems. Get rid of your 2.4GHz phones. Update the firmware after setting up the router(its probably a couple of versions old) This is especially important if you are using one brand router and another brand cards. most important...RTFM!

In addition, most routers also have wired Ethernet ports. I would suggest to connect the cable-modem with a cable to the router, then connect the main PC nearest the router also with an ethernet cable to the router, and only connect the remote PC or laptop with a wireless unit.
Saves a few bucks and you have a better connection. If you can, you should also try to use a cable for the remote PC/laptop, instead of wireless. Your neighbour might "listen in" on your connection, if you don't get the wireless protocols installed correctly.