I have an Acer laptop with an OEM Windows 8.1 originally installed on it. After upgrading to Windows 10 I would need to do a factory reset. If I go to Disk Management, the recovery partition seems to be intact (neither recovery DVD nor product key was provided). However, if I press Alt-F10 as suggested by the manufacturer, I see the Windows 10 recovery environment, but I can't access the original recovery partition that would install back the original Windows 8.1. I'm just prompted to insert Windows installation or recovery media to continue, which I obviously do not have. How could I restore the original Windows 8.1?
Your problems are:
Finding the Windows 8 Recovery partition.
Windows 10 is supposed when installed to update the Recovery partition, but doesn't always do that. Examine the partitions on your disk to see if it's still there, and in that case it might still be visible from the boot menu (normally F12 when booting).
Getting a Windows 8 boot ISO.
You may download boot media from Microsoft. Microsoft is not asking for a serial number before download (at the moment at least).
Installing Windows 8.
The Windows 8 installation will pick the serial number from the firmware where it's baked-in. If the installation doesn't do that, then Windows 8 will do so once it's fully installed.
Drivers for your hardware might be a problem if they are not supplied by the installation, or not found after Windows is fully installed. You may find them on the website of the manufacturer of the computer. You might also try to export your existing drivers in Windows 10, as they might come in handy. See this article on using DISM for that (also some free products are available).
In any case, I would like to really recommend not downgrading from Windows 10, unless for serious reasons like lack of hardware support.