Since you have a mini, your keyboard may or may not have an eject button. I think all Apple keyboards from the last several years should have one.
Since you're new to Mac, I'll tell you there's probably five different ways to do almost anything. Here's several ways to eject a disc:
1.) From the desktop, click and drag the disc icon to the trash can on your dock. When you do, the trash can icon will change into the eject symbol. When the disc icon is over it, the eject symbol will turn dark gray, then let go.
2.) Click one time in the disc icon on the Desktop to highlight it. Then go to the menu bar and choose File/Eject, or press the Command+E keys.
3.) From any open Finder Window (the same as a Directory window, or Windows Explorer in PC-Speak) you should see any mounted CD, DVD, flash drive, etc. listed in the sidebar on the left. Just to the right of the disc name you should see an eject icon (upward pointing triangle with a horizontal line underneath). When you run your cursor over the symbol, it will turn into a gray button with a white eject symbol. click it to eject.
4.) Open Disk Utility in Applications/Utilities select the optical drive or the disc's name listed in the left and click the blue eject button. It's possible that the mini thinks the disc is ejected, in which case it won't be listed by name on the left and when you click on the name of the optical drive, the eject button will be a dull blue rather than a bright blue. If that's the case see below for another way to eject.
That should be more than enough to get your disc out if everything is working properly. If not, shutdown, then press the power button and hold down your mouse button until the disc ejects. I think an alternative method is to hold down the delete key at startup. If it doesn't eject call AppleCare, or visit an Apple Store or authorized Apple service center. If it's only six months old, it should be repaired at no cost in the first year. If you bought an AppleCare Protection Policy, you have three years.
After you get it out, I suggest that you test other discs. I support a large number of Macs and issues like this are fairly isolated. The optical drive usually either works or fails consistently.
Also, commercially pressed discs are fairly reliable, but consumer-burned discs are hit and miss. I always use major brand name discs, but it can still vary from one computer to the next (on PC's too).
Stick with it. It may be a rough transition, but when things start making more sense, hopefully you'll like it. Check out the two links below for help for people migrating from PC and Mac basics:
http://www.apple.com/support/switch101/
http://www.apple.com/support/mac101/
Good Luck.
