I'm planning on doing myself it for the first time soon. I'll be looking for tutorials online. Is there anything I should be particularly careful with? Any tips?

It's my mother's computer that she's complaining is way too slow, it's a facebook machine so there's almost nothing in it, that should make it easier, but if it goes well I'll format my own in the future.

Formatting is easy.
Just don't forget to backup what you want to keep.

Once you back up everything that you don't intend to loose, it's just a matter of starting the format and then simply reinstalling the OS and then drivers and such. Unless you hit a snag along the way, which shouldn't be a direct result of the format, but an underlining and previously existing problem, you should be done with it in a few hours, give or take.

I've done it at least ten times by now, mostly for friends or family.

formatting and reinstalling si easy
i hve done it so often i lost count
what takes the most time however is installing all the security updates

Nobody said anything about reinstalling anything, don't get ahead of yourselves.

If talking about Win7, use Simplix, either post install, or to add the updates to the installation media. No idea for Win8.x, but Win10 should also need a single update to be up to date, since from what I recall it only offers two, last-to-current and first-to-current.

Hardware dependent. If you have access to another computer post install, it shouldn't be a big problem, if you don't have access, best to grab at least the network drivers before hand.

Windows (I assume we're talking a Windows machine here) has a ton of basic drivers. If your mom doesn't have any odd peripheral devices or a dedicated graphcis card, you should be fine with the generic Windows drivers.

Do you have an external HD?
I recommend one.
Drag and copy all the files you (and your mother) consider important, and format the computer.
There's no secret.
If you're worried about drivers take a look at what you have installed right now. :)

i very much doubt he will nuke his mom's pc and then not reinstall

I guess you could put the tires off a car and then be done with it.

look mom you car is all clean but you wont be able to drive with it !

Much safer that way.

If she is using it only for facebook, you can consider trying the linux mint edition.

[url=https://www.linuxmint.com/edition.php?id=218 ]Linux Mint 18 Cinnemon 32 Bit [/url]

Linux Mint 18 Cinnemon 64 Bit

If you are interested, i can teach you how to do a bootable flash drive with that and install it. I did that for my a few of my neighbours (50-60 year age range) and they are very happy about it so far.

I know that was not your question but i wanted to give you options.