How to upgrade an old PC to Windows 10 (14 Jan 2022)

If you have a PC running a "genuine" copy of Windows 7/8/8.1 (Windows 7 Home, Pro, or Ultimate edition, or Windows 8.x Home or Business, properly licensed and activated), you can follow the same steps I did to install Windows 10 as an upgrade.

Before getting started, I recommend a few preliminary tasks that can head off potential problems:

Confirm that your copy of Windows is properly activated. This is especially important if you recently reinstalled Windows.
Check for any recent driver updates, especially for network and storage hardware.
Download and install any available BIOS updates for your hardware; this step is especially important for systems that were originally sold in 2017 or earlier, when hardware makers were still shaking out issues with Windows 10.
Back up your data files to an external hard drive or cloud storage (or both). Consider doing a full system backup to an external hard drive using the Windows 7 backup program, which is also available in Windows 8.x and Windows 10. Just run the command Sdclt.exe, and then choose the Create A System Image option.
Temporarily uninstall third-party security software and low-level system utilities that can interfere with the upgrade. You can reinstall those programs after the upgrade is complete.
Finally, disconnect any unnecessary external devices, especially USB flash drives and external hard drives. (Several common installation errors can be traced to the Setup program being confused by these additional drives.)  

Having an SSD as your system drive is the best way to speed up the following process.

Go to the Download Windows 10 webpage and 
click the Download tool now button
double-click the executable file to run the Media Creation Tool.

You can upgrade directly using this tool, or create separate media.

If you've downloaded the Media Creation Tool on the machine you plan to upgrade, and you plan to upgrade that PC and only that PC, you can choose the 
Upgrade This PC Now
option. That option installs the most recent version of Windows 10. It typically takes about an hour, depending on your hardware. 

If you know you'll want to upgrade to Windows 10 on more than one PC, or if you just want more flexibility in the event that the instant upgrade fails, choose the second option and save the installation files to a USB drive or as an ISO file. The download takes a little time but when it's complete, you can run the Windows Setup program manually to install Windows 10 on any PC running any supported Windows version (sorry, this won't work with PCs running Windows Vista or Windows XP). 

The exact steps depend on which download option you chose:

USB flash drive  Insert the USB flash drive you just created into a free USB slot on the PC you want to upgrade. Then open File Explorer (Windows Explorer in Windows 7) and double-click Setup to install Windows 10. 
Note that you >>> cannot boot from the newly created USB drive <<<
or DVD to perform an upgrade to Windows 10. You must run the Windows 10 setup program from your currently installed and activated copy of Windows.

Follow the prompts to complete the upgrade to Windows 10. You will not be asked for a product key, and when the upgrade is complete and you've connected to the internet, you'll have a digital license to the most recent Windows 10 version, which you can confirm by going to 
Settings > Update and Security > Activation. 
All your apps and data files will be available.

The digital license is associated with that specific device, which means you can reformat the disk and perform a clean installation of the same edition of Windows 10 anytime. (If you're thinking of upgrading your old system drive to an SSD, perform the upgrade to Windows 10 on the old hardware; after confirming that the new Windows 10 version is properly activated, install the SSD and then either restore from a backup image or boot from the USB flash drive to do a clean install. You won't need a product key, and activation is automatic.)