For example: I would like to access an Excel file on my HP from my Acer and edit it from my Acer.
I'm not having any success because when I try to access a file on my HP, I am required to provide a user ID and password for the HP and I have been unable to figure out what those are.
This depends on how you access each PC. If they are both local accounts with the same password, as long as you enable sharing, you should be able to access file on one PC from the other PC.
If you are using different local accounts then you need to give share / give permission for the account on the other PC to access the files.
If you use the same Microsoft account on both PCs together with OneDrive, sharing is easiest.
If you use OneDrive on each PC with different Microsoft accounts, then you need to share the drive (or a folder), with the other Microsoft account.
Sharing and access is also affected by what you tell each system about the network environment. If they both understand that they are in a “safe” home or work network environment, then they will make themselves known on the network. If either PC thinks it is in an insecure environment it will be harder to find /access.
If you want to access files on one PC from the other PC when you are away from home with one of the PCs, then, as another respondent has suggested, TeamViewer is an excellent program to use for remote access.