Anytime a cd gets stuck in a single play machine, simply take a piece of thin cardboard (lottery tickets work great) or a piece of paper folded a few times to make it thicker. This should be about a half inch wide or wider. Insert it into the top center of the cd slot, hold it there and push the eject button. Repeat if the cd does not come out the first time. This is a common problem if you add labels to a homemade cd.
There is a relatively standard procedure when it comes to removing a CD player or stereo from just about any passenger vehicle. You will need a so-called DIN removal tool which will help you dislodge the CD player from the dashboard. For instructions specific to your Hyundai, click here. This site provides stereo removal information on all major makes.