I recently bought a new mac mini (my first mac ever yay) with a 1TB hard drive at 5,400 rpm. the guy at microcenter also sold me a 1TB hard drive at 7,200 rpm and said it shouldn't be to hard to replace. He said first I'd need to back up the OS to a usb thumb drive and then physically replace the hard drive and then some how get the OS onto the new hard drive.
So far I've found a few tutorials online on how to physically replace the hard drive but it seems like a lot more work than I anticipated (ie. http://www.ifixit.com/Guide/Installing+Mac+Mini+Late+2012+Hard+Drive+Replacement/11716/1). Although, it does seem like something I could do.
However, my main difficulty now is i'm having a very hard time finding any help online on how to 'back the OS up on a usb thumb drive' and how I should re-install it once I do put in the new hard drive. He mentioned using time machine but when I open time machine it doesn't give me any options to interact with the USB thumb drive.