So, there is really no way you can put that on a 120 GB SSD. You'd need to start from scratch with a clean install of the OS on the SSD. You don't need an installation disk to do that, you can download the files directly from Microsoft but you need to make sure you attach the product key for your current Windows installation to a Microsoft account in YOUR name, first.
It would require reinstalling everything. The OS, all programs, any game loaders, etc. The actual game files, if you have any, could be left on the old drive but honestly that drive is simply too small to be of much use. 256GB should be the minimum for any Windows OS drive these days. You're probably better off simply using that SSD for storage of your game files, by moving them to the SSD and then pointing your game loader to the new location, and then when you are able to get a larger SSD THEN worry about putting the OS on there.