Unscrew the fastener from the anchor if there is one
Grip the anchor with needle-nose pliers
Pull the anchor straight out if it is loose enough
Twist the anchor gently while pulling
Use a flathead screwdriver to pry the anchor out
Tap the anchor inward slightly if it is stuck, then pull it out
Cut around the anchor with a utility knife if needed
Drill into the center of plastic anchors to collapse them
Push the remaining anchor pieces into the wall if removal is not possible
Patch the hole after the anchor is removed