What was the machine running? AGP on board video, PCI? Does the MB have an AGP slot or on board video?
Assuming the system is running Windows XP or 2000.
The first thing you have to do is go to system manager and uninstall the old card with the old card plugged in the machine. Then use "nasty file remover" or another utility intended to dig out all the old driver files.
Now shut down and install the new card. Reboot and Windows should find it and install ATI drivers. Follow any windows install prompts. If everything works fine leave it alone now.
If some newer applications have video problems got to the ATI site and download the latest video driver. If you try to use the latest ATI Control Panel it requires that MS .net framework be installed on the computer. It's available as a Windows update download. If the machine is using a windows XP version prior to SP1 you may need to update to SP1 also.
You may need to turn off on board video in the bios to get the plug in card to work. It will be under the "advanced setup" section. If you do not know how to setup a bios, DON'T. If it were your machine I would say go ahead and try, but messing up someone elses machine is rude.
There should be a user manual for the PC. Read it, it explains Bios setup. If your friend lost the manual go to the emachine website and down load the manual for that machine. If you can't find the website/download post the PC model number and someone here will help you locate it.