I want to upgrade to Windows 10 through a clean install and I thought about getting a SSD and installing Win10 on it, making it the primary boot option.

I don't necessarily need to remove the OS from my current HDD, I just need to be able to access the files inside it and execute programs without needing to reinstall them.

Is it possible?

I know this is a probably a pretty basic question, but I don't have too much PC knowledge and I've never tried dual boot before to know.

Yes. Just unplug the system drive, install Windows 10 on your new SSD and then connect the old system drive again.

Coincidentally, I had to do this yesterday, to delete an Nvidia update that screwed up and prevented me from loading to the desktop.

You'll have to go into the BIOS and make your SSD the first boot option. This is easy - no, really, trust me, it is - but I'm on a cellphone and can't explain the whole process at the moment.

If you're going to install to a new drive, no need to even uninstall Windows. Just install Windows 10 to the new drive, make it primary and you can even dual boot so you can boot the old OS if needed. You may need to reinstall programs if its not a portable program.

@dopaminous: It is possible, though many previously installed programs won't work without reinstallation. When a program is installed on Windows, among other things, registry keys are created which are unique to the Windows installation. There are also dependencies that are installed, global variables that are set, config files written, etc.

What I did, when upgrading my system drive (C:) from HDD to SDD. Used Acronis True Image 2017 (got it from a Humble Bundle months prior, only for this purpose ;), its wizard automatically does everything.

Other than that, you could leave your old disk plugged and do a Refresh Windows Installation (the one that KEEPS the Apps and Files).

If you don't have tens and tens of applications installed, it's not that much of a hassle to reinstall. Just copy your Documents/%APPDATA% and possibly some registry entries for your old settings.

Just plug in another drive, make it your boot drive and install Windows. My current PC has four hard drives between the ages of 1 and 9 years old.

You will need to reinstall most if not all programs. I use my old drive as the second drive and just reinstalled programs over top the old folders on it. With an ssd you will want most programs on your hdd anyway for space and only your most used programs and games on your ssd. My desktop, documents folders etc are all the same ones from my old drive, you just have to look up how to redirect them. I also have most my games moved to a third hdd and only a few on my c drive.

No problem having to reinstall the programs, I actually wanted to just wipe everything and only save what I use most, since my PC really needs some cleaning, but I don't have anything to backup my files.
But will Steam games work fine? I have some really heavy games to just reinstall. I know the games in my second HDD will work fine, but what about the ones in C:? If they don't work I can just go to "check local data" (something like that), and Steam will recognize them so they work without reinstalling, right?