If you've already upgraded to 10, then you should be fine since the activation works off a hardware ID. I just went through this 2 days ago with my laptop so still fresh in my mind. You have two options
Option1: Assuming you have enough room on the SSD for your whole HDD, just clone the drive to the SSD and then just do a Windows 10 reset. MS says this will reset it to Win 8 if it has a recovery partition (Guessing you have once since its a prebuilt), but from there you could just re-upgrade to 10. If you dont have a Win 8 recovery parition then it'll just reinstall Win10. Your SSD may have come with migration software (samsungs works great) otherwise there are a ton of options out there.
Option 2: Install the SSD and do a fresh install of Windows 10. I'd go with this unless you want to preserve your Win8 recovery partition. The setup is pretty easy.
Step 1: Before installing the SSD, verify if you have Home or Pro edition. This will come up later. Then download Windows 10 on to a thumb drive.
https://www.microsoft.com/en-us/software-download/windows10
Step 2: Remove your HDD, and install the SDD.
Step 3: Boot off the thumb drive you made. You may need to check to see how your bios allows you to boot off it, but since its a bare SSD it may default to the thumb drive anyway.
Step 4: Install the OS. This party is pretty straight forward but there is one hiccup you'll run in to. At one point it'll ask for the product key. There a skip button, don't click on that. Click on the part that says "I don't have a product key". It'll take you to screen that will ask if you want to install "Windows 10 Home" or Windows 10 Pro". If you had Windows 8.1 you'll choose "Windows 10 Home", if you had Windows 8.1 Pro you'll choose "Windows 10 Pro". From that point on it should be a normal install and it'll activate once you connect to the internet.