Tiorunder:
You can use joint compound to fill in the gouges, but to do a top notch job you need to replace the strength of the missing paper. Drywall get's virtually all of it's strength from the paper on each side of it. Paper is very strong in tension, so for drywall to bend, the paper on one side or the other has to stretch. It's paper's high strength in tension that makes drywall a surprisingly strong and rigid material, considering what it's made of.
If it's just the white surface paper that's missing in certain spots, it's not a big deal and you can just paint over the exposed brown paper with a product called "Guardz" that will seal the surface of the rough brown paper, keeping it down while you skim coat over those areas with joint compound.
If it's more than the white surface paper that's missing, then you should apply strips of self adhesive fiberglass mesh drywall joint tape as a replacement for the paper.
Fiberglass mesh drywall tape is also very strong in tension. Apply the strips of mesh in one direction across the areas of missing paper, then paint over that area with white wood glue diluted with enough water to make a paintable consistancy liquid. As the white wood glue dries, it'll bond the fiberglass mesh to the underlying brown paper. Then apply a second coat of fiberglass mesh strips going perpendicular to the first coat, and paint with dilute white wood glue again. The fiberglass mesh layer is now bonded to the existing brown paper, and is a reasonable substitute for the original paper in terms of strength.
Ditto the above paragraph if the surface paper is even missing in places, thereby exposing the gypsum core. You can apply strips of fiberglass mesh and use dilute white wood glue to bond them to the gypsum core, thereby repairing the drywall and restoring it's original strength.
Once you've got your drywall gouges repaired with fiberglass mesh, you need to skim coat over the surface to restore the wall to it's original smoothness. If you're a rank newbie, there are two ways you can do this:
1. Use a very fine tooth "V" notch trowel to trowel joint compound onto the wall. Allow those joint compound ridges to dry. Give the ridges a very light sanding just to flatten out the peaks of the ridges. Then, holding the trowel upside down, fill in the trowel ridges with more joint compound using the un-notched edge of the trowel.
2. Use a less fine tooth "V" notch trowel to trowel joint compound onto the wall, and immediately use a flat regular plastering trowel and a spray bottle to mist the wet joint compound with water and trowel it smooth. By misting the surface of the joint compound with water, you make it easier to trowel smooth.
Try experimenting with both of these methods on the wall before choosing the one that works best for you.
When the skim coat is dry, give it a light sanding to make the wall smooth, touch up any rough areas, sand them smooth, prime and paint.
In both cases, the result is a more or less uniform thickness of joint compound over the entire wall.
And, as with ALL plaster repairs, work with a bright light shining at a sharp angle to the wall to exagerate the roughness of the wall. When the wall looks "Not as bad as it could be" under critical lighting, it'll look better under normal lighting. When it looks OK under critical lighting, it'll look perfect under normal lighting.
