How can I prepare a wall for paint?

Brenda: Yes. You need to "float" the wall.

https://homeguides.sfgate.com/float-drywall-36924.html

I would also recommend using a primer before paint.

Once you repair the holes with mud and sand them smooth you can vacuum off all the dust and then prime with a stand alone primer. Use a straight primer first not a paint/primer combination. If you have to skim coat your walls because of the damage, once it is done, you still follow the same directions. Primer first, then your paint. It may be easier to have a professional come in and give your walls a skim coat rather than doing a skim coat yourself unless you are a pro at drywall repair.

In your situation with no primer or sizing you could have primed and painted over the wallpaper. That is the only time I recommend painting wall paper. Once you have patched and repaired use Kilz primer then paint your color.

Patch all the holes and smooth completely. I would recommend smoothing with a damp sponge rather than sandpaper (less dust and won't destroy surrounding wall). Wipe down entire area with microfiber cloth and woapy water. Once dry, prime and then paint.

Yeah, I don't like the the all in one paints. It's really not primer and paint. Just more paint solids. May work over light colors but may take more than one coat over darker colors. Some Hometalkers said they need up to thre coats for good coverage.