Holes in drywall
If they're kind of small, spackling compound works quite well. I like to use a sharp razor knife and remove the torn drywall paper first. It's ok if this makes the hole a bit bigger--you don't have 'straggler' paper after the touch up. I use a putty knife to fit the situation--a 1" should work for small holes.
For bigger holes, you might need to use some fiberglass mesh tape over them--but I don't think you're 'there'.
A thornier issue is matching the texturing! This is tough. But I found some aerosol cans of "Orangepeel Texture" at home Depot...these things are great! You dial up your setting and spray it on! May not be perfect but it's probably better than trying to match your texture.
-k in Colorado