Dual Core is em64, meaning you can install both 32bit and or 64bit, Core duo is only 32bit, Core 2 duo is both like Dual Core.
Normally, Fedora's installer anaconda would let you do the installation in a graphical environment, and would install "Desktop and productivity" packages by default. Which means you should have a desktop environment like Windows after installation. If it did not do this for you and you did not choose not to install a desktop environment, means you will need to get it on the internet first via command line, then set up repositories, Livna
for sure, then install the drivers for your graphics adapter/card.
So, you should do as previously mentioned and tell us how you intend to connect to the internet for proper instructions, and tell us about the computer, like what type, make, model. Or if you can find the specs as to what all the hardware it contains.