I think what you're asking is: if I just stick in a second card what will the computer do with it? Well, it will idle in the background without crossfire and any software that needs two cards will use the second one too. Otherwise for normal use it'll sit there, waiting. Games wont touch the second card unless it's Xfired; miners and folding@home software will. Your mining software will pick it up and use the card if you tell it to.
When both cards are seated into the mobo and plugged into the PSU, your comp should recognize both cards. Now the trouble starts: you'll need to download a graphics driver to let the cards talk effectively with the computer. I don't know what the current 'miner accepted' driver is, but I have a feeling it's Catalyst Control Center version 13.1. You'll also need to download the OpenCl APP SDK version 2.6. If you're lucky, it'll all work the first time. Otherwise you'll be tinkering with software for a while trying to figure out.
See, when I built my miner I had to put in card #1 and leave the other one out while I installed all the software. Then I put card 2 in and let that auto-install, then I did the mining software tinkering. If I had two cards in without a driver the machine would crash when I tried to install it. That's the magic of 'will it work, God I hope so' computer tech

Do you have a friend that can help you with this sort of thing? It'll help
enormously and save you from having to live your life on the forums.