Installing a hard drive is a five minute job for somebody who knows what they're doing and white man's magic for someone who doesn't have a clue. If you type "install hard drive" into google it will provide a myriad of sites which provide step by step instructions. You can peruse any one of them and decide whether you are up to the job before committing yourself. There is certainly nothing special required in the way of mechanical aptitude, as proven by the fact that I've done it.
But if your parents' computer really is out of the ark, it may not be quite as simple as just buying a new hard drive. If you post the specs of the system here somebody with more knowledge than I will be able to tell you whether the motherboard may be too old to make the exercise worthwhile.