To those who have turned their old HDD to External ones -

Normally you buy a case for your "formerly internal" HDD to turn it into an external HDD.

With this case it's as simple as "open case", "plugin HDD", "fix HDD with srews or w/e", "close case", "plugin case to your pc (USB /SATA/...), "plugin case to power if neccessary", "done"

Nothing is hard if you are willing to learn. Sir James Dalikkus Villington to Learnz 1858

I have only done 2.5". Complete it in like 5 minutes. (I'm picturing it for you.) I saw 3.5" too but never actually done it.
For 2.5" (laptop-size HDD, first yon need an external enclosure or SATA to USB 3.0, kind of like that) then

1. Plug it in to your HDD. Then it look like this.
2. Test it. It should work fine out of the box. You might want to reformat/partition it but well, the USB work. Deal with those later.
3. Put it in the box This depends, may require some screws, bumper, etc. See manual of your enclosure. (you should unplug your USB first, of course)

Edit: For 3.5 , I did something like this a while ago. Buy the bay, plug in USB and power, put your HDD in. This work with both 3.5" and 2.5" but not recommended for permanent use.

It's very straightforward, as others have already explained. Just make sure you get a compatible case, depending on whether the old drive is IDE or SATA.

No. You just need an enclosure. The difficulty is getting the old files across, and using the proper enclosure. It depends on whether it's a desktop (3.5") or a laptop (2.5") drive. Then you'll want a mSATA enclosure if your machine has one, otherwise USB 3.0. Most enclosures are pretty plug and play, so you don't need to install any drivers or anything.

Technically you don't even need an enclosure. A friend has this cable, it has three prongs, for different types of hard drives, and the other end is USB and I think it has a power split-off. Anyway, all he does it plugs a hard drive up to it, and bam, his computer mounts it like an external. I'd love to have about six of those cables around the desk, just grab one at random and slam a hard drive up.

External's just an internal in a case.

Age don't matter, either. My first kid will have built their very own computer by their 10th birthday (with supervision of course).

i think the upcoming generations will handle these kind of things way better than we do today.
think back hen you was a child, mom and dad han no idea how these little thingies work, and since they are expensive,
there was no intention to find it out at all. but we, with our childish curiosity,
not caring for money or consequences, pulled open the rig and learned.
we grew older, the world got more technologised, today little kids are running around with iphones all the day,
tablet shit, are socially dislocated and are totally happy with that.
as i would say, these are the prerequisites, and all are met!
to the op: it´s really hard to do it wrong, considering the helpful post of brianmwit even more now.
i would suggest you show your mother how simple it really is, and dont forget the "learning for future" argument ;)

There are a number of different types of enclosures you can get to make an internal hard drive into an external hard drive.
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007705&IsNodeId=1&Description=drive%20bay&name=External%20Enclosures&Order=BESTMATCH

But there are a few things to consider.

Does the hard drive you are removing contain the Operating System for the computer? If it does you will not be able to move it to an external case. Your best bet would be to either buy an external hard drive already setup in a case, or buy the hard drive and external enclosure and put it together yourself. Doing it yourself can be good in that you can control the make of the hard drive you get. It lets you get either a fast drive with good warranty but not as much space, or lets you get an almost as fast with an ok warranty but much more space.

Are you going to be running it all the time? If yes then you should invest in an enclosure with a fan to help keep the drive and internals of the enclosure cooler. If only using it long enough to get some files off it, and then turn it off the a simple metal enclosure will. I've had my one on all day and it was quite warm to the touch but was still fine. When doing things with it for long periods of time I would have preferred to have one with a fan in it.

Will you be moving it around a lot? If so a small enclosure and something with some grip on the outside are a good idea. If not then doesn't really matter.

Do you have USB2 or USB3 or E-SATA or some other external connector? USB2 is most common every system has it. USB3 is newer and much faster then USB2, but should be in all newer systems that are a year or 2 old, anything older though and you might not have it. It looks just like a USB2 slot but it should generally be blue. E-SATA is not as common but much faster then USB2. Don't remember if its the same speed or faster then USB3.

If you go with making your own setup, you have to consider how big you want the drive. The external drive bay you pick might have a size limit of the drive. 2, 3 or 4 TB in size.

The enclosure I have was a simple metal one with a power switch on the back of it. The power block plugs into the wall or what ever, and the USB2 cable plugs into the back of the computer case. It came with both the USB2 and power cable but I ditched the short cable it came with for a much longer one so I could have more options on where to put it.

My suggestion would be to either buy an external drive already setup or by a hard drive and enclosure and set it up yourself. You can then move all the unnecessary files from the hard drive in the computer to the external bay.