Anyone know how to use drywall anchors?

Match the anchor to the weight. The little plastic expansion ones are for light stuff, a small frame or a hook. For shelves, mirrors or a TV bracket you want self drilling threaded anchors at least, or toggle bolts for anything properly heavy. For the plastic ones: drill the hole size printed on the pack, tap the anchor in flush, then screw in. The usual mistake is drilling too big and then it just spins. If you hit a stud while drilling, forget the anchor and screw straight into the wood, that's stronger than any anchor.