Smaller holes (anything less than a ½ inch) caused by nails, wall anchors, or coaxial cables, can easily be fixed with just some spackling paste and sandpaper.
Here's a tip: If you have any wall anchors in place that aren't easily removed, don't worry about pulling them out. Doing so will likely just shred the drywall and create an even bigger and messier hole.
Instead, use a utility knife to cut off the exposed plastic collar of the anchor. Then, take a screwdriver with a head slightly smaller than the anchor, and use a hammer to gently tap the rest of the anchor a bit further into the wall. If you're dealing with any plastic or metal self-drilling anchors, use your utility knife to carefully cut and remove a small amount of drywall around the collar of the anchor, just enough for you to screw it into the wall an 1/8 of an inch.
This technique allows you to deal with a much shallower hole, and the now-depressed anchor will give your spackle the support it needs.