TO: The OP
Hello! Given your lack of knowledge of Macs, I will try to keep this as simple as possible for you.
Macs ran from 1996 through 2006 on a Central Processing Unit (CPU) called the PowerPC. Windows software ran on the Intel CPU platform. Apple made the decision to switch its complete inventory of Macs to Intel in 2006, but did not want to financially penalize its existing base of users who had a substantial financial investment in their existing PowerPC software.
So Apple licensed a third party technology, which they called Rosetta and installed it in OS X (at that time Tiger, then Leopard, then optionally Snow Leopard), which transparently and almost magically emulated the PowerPC CPU instructions on the Intel CPU. Rosetta worked so well that most Mac users had no idea what it was, or what it was doing for many years after 2006.
The problem is that Apple's license to continue to develop, install and use Rosetta for OS X expired with the release of Lion and now Mountain Lion. Hence, older PowerPC applications will no longer run natively on Lion or Mountain Lion.
The best solution, if it is available, is an upgrade for your PowerPC software that has been rewritten to work on the Intel CPU. If this upgrade is available, there is generally a financial cost to purchase it and many such upgrades are very costly, especially cumulatively. Presumably, Corel was never rewritten to work on the Intel CPU.
Since it appears that you have purchased a new Mac, it must boot Mountain Lion, so another alternative, the so-called "dual-boot" approach, is not available to you.
That leaves using what is called virtualization on your Mac to be able to run this software.
One solution is to run Windows on your Mac (either in what is called Bootcamp, or in virtualization through the use of a third party program offered by Parallels or VMWare Fusion). Is there a Windows version of Corel that you would be happy and satisfied to run? You would have to purchase Windows and presumably the Windows version of Corel as well.
Another solution is to run Mac OS X Snow Leopard in virtualization on your Mac. This is the version of OS X that just preceeded Lion and Mountain Lion and is the last one that can have Rosetta installed into it.
Parallels and VMWare Fusion only support the installation of a version of Snow Leopard called Snow Leopard Server. While it is easy to install and is supported, it originally sold by Apple for $499+. While Apple no longer sells it, it is available on eBay and I have seen it selling recently for $51 - $99+. Parallels and VMWare Fusion each sell for about $79 retail and shopping on the internet can yield some discounts. You only need one or the other, not the both of Parallels or VMWare.
There is also a free virtualization program offered by Oracle, called VirtualBox. I have no experience with this program and I do not know if Snow Leopard or its Server version can be installed on it.
A more complicated approach is the installation of the normal Snow Leopard into Parallels. Apple still sells Snow Leopard for $19.99, but you would have to follow the installation instructions I have offered online. This may be too challenging for you to undertake, but the instructions are located here:
http://forums.macrumors.com/showthread.php?t=1365439
You can also download a 14 day free trial of Parallels here:
http://trial.parallels.com/index.php?lang=en&terr=us
It will look something like this on your iMac (and the Snow Leopard screen can be enlarged to encompass the complete screen; it is minimized here to show that Lion is running in the background):

[click on image to enlarge]
I am sure you will have questions; so let me know what they are...