Replacing both are really straight forward to do. Getting the files from the original drive on to the new one can be a tricky.
If the current hard drive is working then I suggest you get an external USB hard drive enclosure for it. They are usually available for less than $20. This would allow you to boot from the old drive, connected via USB, and restore everything with a program like Carbon Copy Cloner. If you are already backing your computer up with Time Machine to an existing external drive then that's even easier.