So, I'm considering getting an new hard drive, SSD one this time. But before I splash the cash, I want to know if it's possible to, uhm, move my OS to this new drive or do I need to do a full reinstall? I've never done this before, so any advice is appreciated.

you just can move the OS to the SSD very easily. Most of the SSD even come with a program for this purpose but funnily enough for me for example that Acronis True Image which came with my SSD didn't work (as it always wanted to copy all 3 partitions on my maindrive and not only the OS partition - i guess that was the issue) so i ended up using this freeware in the end :
https://www.partitionwizard.com/free-partition-manager.html - took like 15 minutes in total - then you only need to change your boot sequence in the BIOS and you are good to go.

Yes it is possible, given of course that you current system disk fit on the new SSD (for example if your C dirve contains 500GB of data you won't be able to fit it to a 250GB SSD) and that it's not encrypted. (i.e. Bitlocker)

Then you need to use a partition copy tools. Personally I use the Acronis one but it's not free, there are some free ones that are supposed to work as well but I haven't tested them.

I too have used Acronis however it was free for me as it came with my Intel SSD drive. I've used it to transfer an OS from one HDD to another, and HDD to SDD. So far every time I've used it it worked perfectly with no problems.

If you don't get a free copy with your drive and can't find one for free directly from Acronis or through some other vendor such as Western Digital or others (some used to have free copies on their own sites), then you might possibly be able to use some OSS software such as Mondorescue or Clonezilla or similar, not sure.

Assuming that OS is some flavor of Linux, it should be fairly simple to move it to a new drive. Something the following should work:

1. Copy all files from the root to the new drive. (Only copy the root partition, and don't copy things like /proc, /dev, /sys, and /run)
2. Install GRUB on the new drive

Alternatively, you could, if you're careful, use dd to copy the image of one drive to the next one.

Note that, if you are using a proprietary OS (Windows comes to mind), this likely will not work, and you will likely need to do a new install.

Most retail SSD's will come with a migration software ( on disk or downloadable from a website). I recently did it for 2 computers . On mine, with a Samsung drive, came with a proprietary software, on a friend's with a Crucial drive, came with Acronis True Image. In both cases, the whole process was completed with a few clicks. Samsung also provides a software that optimizes your OS .

Not true, as mentioned by almost every reply before yours. Acronis True Image is one piece of software for doing this in Windows flawlessly, but there are others as well.

Are these softwares easy to use?

The Samsung one is very easy ( but will only work with a Samsung drive ) , and functions very much like an assistant. Basically it creates an image of your current drive on the SSD, and allocates the additional space as free space to the main partition ( just to give an idea : https://www.youtube.com/watch?v=2SnXYVSDoVQ).

Acronis offers some more option, but the automatic mode is basically the same procedure
https://www.youtube.com/watch?v=KlXkYKzY6vs

Note you also need an external enclosure ( usb externl box, the simplest the best) in which to initially place your new ssd, then connect that to the computer, perform the migration ( takes some time though), then remove your ssd from the enclosure and install it in the PC.

Need a what in a what now?

Is there a reason why you can't just re-install. Personally I would re-install at any needed time, Windows is poor at self maintenance at the best of times, so a good clean install fixes that. I have tried in the past to copy an OS from one machine to another, forget which program, but it didn't work. The hardware was different, but it just didn't work. So personally I would install a fresh install onto the new hardware. It hardly takes that much time nowadays (espcially if you create a CD with all the necessary drivers and additional software.

in order to clone your existing drive, you need to first connect your new SDD to the PC, the easiest way being an external USB box (enclosure) ( example https://www.amazon.fr/Inateck-externe-disque-Compatible-Windows/dp/B00DW374W4/ref=sr_1_4?s=computers&ie=UTF8&qid=1470750983&sr=1-4) or an USB adapter .

That would require I'd install everything again. I'd much rather just transfer the OS to the new drive, if it's easily doable. Every time before this I have done a clean install and every time I've had problems with it.

And I don't have a install disc for Win 10.

Since eventually you have to plug the ssd in the PC, what if you do it in the first place? Surely any of these cloning programs will detect the plugged disk... or not?

Yes, it's easier to just clone your disk, but in case you end up having to reinstall Windows 10 don't worry about the install disk. Almost nobody in the world has one :-D. I haven't tried it yet, but in theory you can download the disc from Microsoft, and then it should install without a key or anything as long as it's the same computer.