I know where the AppCenter is, and know how to download them, but I cant find the things to actually use the,. Obviously I am new to elementary OS. If I want to use, say Abiword, where is the icon to click on?
elementary does not have an active desktop by default. Therefore you will not see applications and/or other files available there. You can find them in the Slingshot menu, assuming you have already installed them, which is like the Start menu on Windows. This menu can be accessed by clicking on the icon in the top left of the screen (or by pressing the Windows key + Space) and searching through the items listed (they are sorted alphabetically).
Just go in app center and search by "abiword". You can press the button free in its front or click in the icon and press free. If the app has price, you can click on the triangle, and put 0 and press enter and the app will be download free.