When you buy a new internal hard drive (HDD) or solid state drive (SSD
), it's usually blank. So, you need to get an operating system (Windows, Ubuntu, Mac OSX, etc.) on it.
You can copy ALL the data from the old drive to the new. Which means your system will be exactly the same, only on a new drive. For more info, search for "drive image" or "clone".
You can also perform a fresh OS install on the new drive. If you have a USB CD/DVD reader and a OS installation disc, just load the disc, plug in the reader, and set the Mini to boot off CD (I think you press 0 (zero) at the Dell splash screen when powering up to access the boot device menu). Then follow the OS's installation process, it's usually straightforward.
The downside of a fresh install is that you'll need to install applications again and transfer data files over from the old drive. The upside is that you lose any old garbage accumulated on the old drive.