How do I make shelf liner stick to my walls like wallpaper?

If you use it, use silicone wallpaper glue. It will stand up better. Have fun!

You would need to use wallpaper paste. Coat the back of the paper with wallpaper paste and hang it like regular wallpaper.

Get wall paper glue

Williams right. If its vinyl, use vinyl wallpaper paste.

You can use wallpaper adhesive found at any hardware store. Here is my video I did on wallpapering, it has a guide to help you. https://www.simplenaturedecorblog.com/dining-room-wallpaper-ideas-video/

It is a nightmare to remove because of the vinyl top. We purchased a fixer upper back in the eighties and the small entryway and stairway walls to the basement were done in contact paper and made it look like a whore house (bright red and white pattern. If it hadn't been such a good deal, I would never have bought the place because of the contact paper. It took me days to remove it. Make sure that it looks good as wallpaper before you put the whole up.

Although it 'is possible' to apply contact paper to walls, I would dissuade you from doing this. The removal will probably be a slow frustrating process, and will most likely damage the drywall underneath to some extent.

Re-read about Nancy's first hand experience.

I just bought the very same ones as the OP .

I figured it was cheap enough ,$1.25 at Dollar Tree , that I could redo it if needed .

I would not wallpaper nor apply shelf liner to your Dad's walls. Most homebuyers do not want wallpaper nor the aggravation of removing it.