Remove any screw from the anchor
Grip the anchor with needle-nose pliers
Pull the anchor straight out if it loosens easily
Twist the anchor gently while pulling
If it will not come out, push it into the wall cavity
For plastic anchors, pry the edge with a flathead screwdriver
For toggle bolts, remove the bolt and push the toggle through the hole
For molly bolts, collapse the sleeve inward and pull it out
Fill the hole with spackle or wall filler
Sand the patched area smooth after it dries