Remove the screw from the anchor
Grip the anchor with pliers and pull it out
If it will not pull out, gently twist while pulling
If the anchor breaks off flush, push it into the wall
For plastic anchors, cut around the edge with a utility knife if needed
For metal anchors, collapse the anchor inward with a screwdriver or punch
Patch the hole with spackle or joint compound
Sand smooth after it dries
Prime and paint the repaired area